How do you solve the equation $x^{2} - 8 x = - 9$ $x^2-8x=-9$ by completing the square?

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How do you solve the equation $x^{2} - 8 x = - 9$ $x^2-8x=-9$ by completing the square?

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Answer 1 · 2017-03-19T05:33:54

$x = 6.64575131 or x = 1.35424868$ $x=6.64575131 or x=1.35424868$

Explanation:

$C o m m e n c i n g$ $color(red)(Commenci ng)$ $c o m p l e t i n g$ $color(red)(compl e ti ng)$ $t h e$ $color(red)(the)$ $s q u a r e$ $color(red)(squ are)$ $m e t h o d$ $color(red)(method)$ $n o w,$ $color(red)(now,)$

1) Know the formula for the perfect quadratic square, which is,

${(a x \pm b)}^{2} = a x^{2} \pm 2 a b x + b^{2}$ $(ax+-b)^2 = ax^2+-2abx+b^2$

2) Figure out your $a and b$ $a and b$ values,

$a =$ $a=$ coefficient of $x^{2}$ $x^2$ , which is $1$ $1$ .
$b = \frac{- 8}{2 (1)} = - 4$ $color(red)(b=(-8)/(2(1)) = -4)$

3) Add $b^{2}$ $color(red)(b^2)$ on both sides of the equation, giving you an overall net of 0, hence not affecting the result of the equation,

$x^{2} - 8 x + {(- 4)}^{2} = - 9 + {(- 4)}^{2}$ $x^2-8x+color(red)((-4)^2)=-9+color(red)((-4)^2)$
${(x - 4)}^{2} = 7$ $(x-4)^2=7$

4) Square root both sides,

$x - 4 = \pm \sqrt{7}$ $x-4=+-sqrt(7)$

5) Add $4$ $4$ on both sides,

$x = \pm \sqrt{7} + 4$ $x=+-sqrt7+4$

6) Calculate the two values of $x$ $x$ ,

$x = 6.64575131 or x = 1.35424868$ $x=6.64575131 or x=1.35424868$

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How do you solve the equation $x^{2} - 8 x = - 9$ $x^2-8x=-9$ by completing the square?

1 Answer

Explanation:

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How do you solve the equation $x^{2} - 8 x = - 9$ $x^2-8x=-9$ by completing the square?