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

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Answer 1 · 2017-03-19T05:33:54

$x=6.64575131 or x=1.35424868$

$color(red)(Commenci ng)$ $color(red)(compl e ti ng)$ $color(red)(the)$ $color(red)(squ are)$ $color(red)(method)$ $color(red)(now,)$

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

$(ax+-b)^2 = ax^2+-2abx+b^2$

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

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

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

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

4) Square root both sides,

$x-4=+-sqrt(7)$

5) Add $4$ on both sides,

$x=+-sqrt7+4$

6) Calculate the two values of $x$ ,

$x=6.64575131 or x=1.35424868$

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