Question

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

Answer 1

`x=6.64575131 or x=1.35424868`

Explanation:

`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`