How do you solve $x^{2} - 24 x = 10$ $x^2-24x=10$ by completing the square?

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How do you solve $x^{2} - 24 x = 10$ $x^2-24x=10$ by completing the square?

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Answer 1 · 2017-10-22T16:23:05

$x = 24.4097, - 0.4097$ $x = 24.4097, -0.4097$

Explanation:

$x^{2} - 24 x = 10$ $x^2 -24x = 10$

$x^{2} + (2 (x) (- 12)) = 10$ $x^2 + (2 (x) (-12) ) = 10$

$x^{2} + (2 (x) (- 12)) + 144 - 144 = 10$ $x^2 + ( 2 (x) (-12) ) +144 -144 = 10$ (Add and subtract 144)#

$x^{2} + (2 (x) (- 12) + {(12)}^{2} = 154$ $x^2 + ( 2 (x)(-12) + (12)^2 = 154$
${(x - 12)}^{2} = 154$ $(x-12)^2 = 154$
$(x - 12) = \pm \sqrt{154} a a a$ $(x-12) = +-sqrt 154 color (white)(aaa)$ taking square root on both sides
$x = 12 \pm \sqrt{154}$ $x = 12 +- sqrt154$
$x = 24.4097, - 0.4097$ $x = 24.4097, -0.4097$

Answer 2 · 2017-10-22T16:28:50

$x = 12 \pm \sqrt{154}$ $x=12+-sqrt(154)$

Explanation:

Completing the square means making the $x^{2}$ $x^2$ and $x$ $x$ terms take the form $x^{2} + 2 n x + n^{2}$ $x^2 +2nx +n^2$ . Where in this case $n = - 12$ $n=-12$ .

So, $x^{2} - 24 x = 10$ $x^2-24x=10$ becomes $x^{2} - 24 x + 144 = 10 + 144$ $x^2 -24x+144=10+144$ .
So, ${(x - 12)}^{2} = 154$ $(x-12)^2=154$
$x = 12 \pm \sqrt{154}$ $x=12+-sqrt(154)$

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How do you solve $x^{2} - 24 x = 10$ $x^2-24x=10$ by completing the square?

2 Answers

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How do you solve $x^{2} - 24 x = 10$ $x^2-24x=10$ by completing the square?