Question

Find the solution set. (x+9) (x+9) = 0

Answer 1

The solution set is
`x=-9`

Explanation:

we have

`(x+9)(x+9)=0`

we know that

`(x+9)(x+9)=x^(2)+18x+81`

so

`x^(2)+18x+81=0`

The formula to solve a quadratic equation of the form
`ax^(2) +bx+c=0` is equal to

`x=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}`

in this problem we have

`x^(2)+18x+81=0`

so

`a=1\\b=18\\c=81`

substitute in the formula

`x=\frac{-18(+/-)\sqrt{18^(2)-4(1)(81)}} {2(1)}`

`x=\frac{-18(+/-)√(0)} {2}`

The radicand is equal to zero, therefore, the solution has only one real solution

`x=\frac{-18} {2}=-9`