Question

How to solve x^2+24x+90=0 by completing the square? Can someone show me the steps to solve this?

Answer 1

x^2+2*12x+(12)^2 - (12)^2+90 = 0

Answer 2

I'm lost.

Answer 3

\[x^2+2*12x+(12)^2 =54= ( 3 \sqrt 6)^2
\]

Answer 4

You have an equation of the form \[x^2+bx+c=0\]To complete the square, calculate \[\left({b\over 2}\right)^2\]And then add and subtract this from your original equation. So now you have \[x^2+bx+{b^2 \over 4}-{b^2 \over 4}+c=0\]This factors as \[(x+{b \over 2})^2-{b^2 \over 4} +c=0\]

Answer 5

(12)^2 - (12)^2 =0 so you added zero and nothing changes

Answer 6

\[(x+12)^2 = (3 \sqrt 6)^2\]

Answer 7

Noe you can finish t.

Answer 8

By plugging in \(b=24\) and \(c=90\), you can solve\[(x+{b \over2})^2-{b^2 \over 4}+c=0\]For your question.

Answer 9

is it x+12=36? and then you just solve it?

Answer 10

I f \[ A^2 = B^2
\]
tehn \[ A = \pm B \]

Answer 11

I don't get it?

Answer 12

\[ x+12 = \pm 3 \sqrt 6\]

Answer 13

Oh ohkay. How would I go about solving that?

Answer 14

There are two roots
\[ x= -12 - 3 \sqrt 6, \quad x= -12 + 3 \sqrt 6,
\]

Answer 15

Thank you! :D

Answer 16

As @KingGeorge described before, this how one proves the quadratic formula.