How do you solve $8x=x^2-9$ using the quadratic formula?

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Answer 1 · 2018-03-10T18:03:23

See a solution process below:

First, subtract $color(red)(8x)$ from each side of the equation to put the equation in standard quadratic form:

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

$0 = x^2 - 8x - 9$

$x^2 - 8x - 9 = 0$

We can now use the quadratic equation to solve this problem:

For $color(red)(a)x^2 + color(blue)(b)x + color(green)(c) = 0$ , the values of $x$ which are the solutions to the equation are given by:

$x = (-color(blue)(b) +- sqrt(color(blue)(b)^2 - (4color(red)(a)color(green)(c))))/(2 * color(red)(a))$

Substituting:

$color(red)(1)$ for $color(red)(a)$

$color(blue)(-8)$ for $color(blue)(b)$

$color(green)(-9)$ for $color(green)(c)$ gives:

$x = (-color(blue)(-8) +- sqrt(color(blue)(-8)^2 - (4 * color(red)(1) * color(green)(-9))))/(2 * color(red)(1))$

$x = (8 +- sqrt(64 - (-36)))/2$

$x = (8 +- sqrt(64 + 36))/2$

$x = (8 - sqrt(100))/2$ ; $x = (8 + sqrt(100))/2$

$x = (8 - 10)/2$ ; $x = (8 + 10)/2$

$x =(-2)/2$ ; $x = 18/2$

$x =-1$ ; $x = 9$

The Solution Set Is:

$x ={-1, 9}$

How do you solve 8x=x^2-98x=x^2-9 using the quadratic formula?