give the quadratic funtion f(x)=9x^2+36x+36 find the value of x such that f(x) =9must show work

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beckden | High School Teacher | (Level 1) Educator

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We want to solve the equation

`9 = 9x^2 + 36x + 36`   wrtiting in standard form we get

`9x^2 + 36x + 27 = 0`

Factoring we get

`9(x^2 + 4x + 3) = 0`

This can be factored into

`9(x+3)(x+1) = 0`

So using the zero product property we get

x = -3 or x = -1 as the answer to the question .   we can check

`f(-3) = 9(-3)^2 + 36(-3) + 36 = 81 - 108 + 36 = 117 - 108 = 9`

`f(-1) = 9(-1)^2 + 36(-1) + 36 = 9 - 36 + 36 = 9`

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