Question

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

Answer 1

See a solution process below:

Explanation:

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:

The quadratic formula states:

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}`