Can someone tell me what im doing wrong when completing the square?

[anikan_sw]

I keep doing the problem like the formula says but I keep getting the wrong answer The problem is m^2-3=-m

21. m^2 -3=-m

m^2 +m-3=0

m^2/1 +m/1=3/1

m^2+(m/2)^2=3

m^2 +m+0.25=3 + 0.25

m^2 + m +0.25=3.25

(m+0.5)^2= square root of 3.25

m+0.5= square root of 3.25

and thats where I get stuck because when I look in the back I see im way off. Can someone explain what im doing wrong. It would be a big help.

[iNow]

It looks like you need to factor at your second step using the quadratic formula:

 

 

[math]x = {\frac{-b \pm \sqrt{b2 - 4ac}}{2a}}[/math]

 

 

Except, in your case, instead of solving for x, you are solving for m (no difference, really).

 

 

In your equation, both A and B = 1, and C = what?

[Bignose]

It looks like you need to factor at your second step using the quadratic formula:

 

 

[math]x = {\frac{-b \pm \sqrt{b2 - 4ac}}{2a}}[/math]

 

 

Except, in your case, instead of solving for x, you are solving for m (no difference, really).

 

 

In your equation, both A and B = 1, and C = what?

 

Just some small points here... that definitely needs to read b^2 in the LaTeX:

 

[math]x = {\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/math]

 

And secondly unless you define what a, b, and c are, this isn't much help.

 

a, b, and c come from the equation

 

[math] a x^2 + b x + c = 0 [/math]

 

whose solutions are given by the equation above.

[iNow]

 

It's amazing what one missed key stroke can cause when doing math. Thank you for the correction.

 

Per the defining of A, B, and C, I'd hoped to cause our friend to do some further research on his/her own, but I concede your point.

 

 

 

 

Did this suggestion (with correction) help point you in the right direction, anikan?

[timo]

Why do you think your were doing something wrong? Everything looks fine; including your result, which is [math]m= \sqrt{3.25}-0.5[/math].

EDIT: Well, not completely. When taking the root, you'd not only get m+0.5 = sqrt(3.25) but also an additional solution m+0.5 = -sqrt(3.25).

[anikan_sw]

Were not supposed to solve this using the quadratic equation. It's supposed to be done by completing the square using the formula-

ax^2 + bx +c=0

x^2 +bx/a = -c/a

[Cap'n Refsmmat]

Well, your answer is right, except for the detail Atheist noted -- there are two solutions.

[the tree]

Before my A-Levels, there were two maths classes that were basically working at the same level, the other classes teacher put a lot more emphasis on completing the square than my teacher. When we got to A-Levels and we were all in the same class this somehow become an aspect of a token rivalry, "completing the square is for chumps". So whenever I helped younger students (especially when someone who used to be in the rival class was around) I would repeat this along with one simple fact: you never ever ever have to complete the square.

[anikan_sw]

Thanks for the help everyone.

[lakmilis]

well ok, u gave a form u wish to obtain by completing the sqaure....

 

 

to complete the square u do this:

 

 

(m + 1/2)^2 = -11/4

 

 

is that enough? or do u wish now to proceed and take the root on each side etc etc?

[Country Boy]

I keep doing the problem like the formula says but I keep getting the wrong answer The problem is m^2-3=-m

21. m^2 -3=-m

m^2 +m-3=0

m^2/1 +m/1=3/1

m^2+(m/2)^2=3

You are following a formula? surely it doesn't say "replace m/1 with (m/2)^2! They aren't equal and you can't do that. I imagine what you are doing is dividing the coefficient of m by 2 and squaring that: (1/2)^2= 1/4, not (m/2)^2 and it doesn't go into the middle of the equation.

 

m^2 +m+0.25=3 + 0.25

Okay, now you are back on track!

 

m^2 + m +0.25=3.25

(m+0.5)^2= square root of 3.25

m+0.5= square root of 3.25

and thats where I get stuck because when I look in the back I see im way off. Can someone explain what im doing wrong. It would be a big help.

Since you don't say what is in the back of the book that is "way off", I don't know what you did. You have completed the square when you write m^2+ m+ 0.25= 3.25 or (m+ .5)^2= 3.25. But what was the problem really? To solve the equation? In that case, you need to recall that there are two numbers whose square is 3.25: m+ .5= +/- sqrt{3.25} and the solutions to the equation are m= -.5 +/- sqrt{3.25}.

[lakmilis]

bleep

---

Merged post follows:

Consecutive posts merged

well ok, u gave a form u wish to obtain by completing the sqaure....

 

 

to complete the square u do this:

 

 

(m + 1/2)^2 = -11/4

 

 

is that enough? or do u wish now to proceed and take the root on each side etc etc?

 

Oh dear.. it's a year on.. but of course it should of been 13/4 on the right.. .not -11/4 LOL .. jees.. how did I do that?

Edited March 27, 2009 by lakmilis
Consecutive posts merged.

[cameron marical]

m^2 +m-3=0

 

you can use the diamond method i think. so itd be something roughly {m-1.73}{m+1.73}

 

1.73 is actually 1.7320508075688772 though, if you want it really specific.

[max.yevs]

you can use the diamond method i think. so itd be something roughly {m-1.73}{m+1.73}

 

1.73 is actually 1.7320508075688772 though, if you want it really specific.

 

 

no cameron, sorry

[math](m-1.73)(m+1.73) = m^2 - 1.73^2 = m^2 - 3[/math]

 

but he was factoring [math]m^2 + m - 3[/math]

 

you can't solve it by simple factoring because 3 only has two factors: 1 and 3; and the difference between them is 2, but the coefficient of m is 1, not 2. the roots are irrational. completing the square is impossible.

 

only thing left to do is use the quadratic formula:

 

[math]{\frac{-1 \pm\sqrt{1^2 - 4(1)(-3)}}{2(1)}}[/math]

[math]{\frac{-1 \pm\sqrt{13}}{2}}[/math]

which calculated gives [math]m = -1/2 \pm{\frac{\sqrt{13}}{2}}[/math]

 

so, [math]m = 1.30277563, -2.30277563[/math]

 

 

And for all of you who got other answers: when you complete the square all the terms and constants have to stay on one side.

 

Below is a picture prooving my answers... (fooplot)

Edited March 28, 2009 by max.yevs

[cameron marical]

ohh............

 

 

[lakmilis]

no cameron, sorry

[math](m-1.73)(m+1.73) = m^2 - 1.73^2 = m^2 - 3[/math]

 

but he was factoring [math]m^2 + m - 3[/math]

 

you can't solve it by simple factoring because 3 only has two factors: 1 and 3; and the difference between them is 2, but the coefficient of m is 1, not 2. the roots are irrational. completing the square is impossible.

 

only thing left to do is use the quadratic formula:

 

[math]{\frac{-1 \pm\sqrt{1^2 - 4(1)(-3)}}{2(1)}}[/math]

[math]{\frac{-1 \pm\sqrt{13}}{2}}[/math]

which calculated gives [math]m = -1/2 \pm{\frac{\sqrt{13}}{2}}[/math]

 

so, [math]m = 1.30277563, -2.30277563[/math]

 

 

And for all of you who got other answers: when you complete the square all the terms and constants have to stay on one side.

 

Below is a picture prooving my answers... (fooplot)

 

hehe... ocmpleting the square is *not* impossible: completing the square means adding 1/4 to each side.

 

thus [MATH](m+1/2)^2 = 13/4[/MATH]

 

completing the square is a means to make it easier to look at so to speak, thus the numerical solution is not so interesting (apart from if one is solving an actual problem).

[the tree]

True, I think what Max meant was that since you can't take the roots in your head, then completing the square is impossible without doing so much computational work as to make it pointless.

 

Completing the square is supposed to be a neat little trick, appropriate in some cases, but not generally.

 

On another note, why has this thread been dragged up again?