Question

Solve the equation involving absolute value. Type you answers from smallest to largest. If an answer is not an integer then type it as a decimal rounded to the nearest hundredth. |x^2+2x-36|=12 x=Answer, Answer, Answer and Answer

Answer 1

Given:

The euqation is,

`|x^2+2x-36|=12`

Step-by-step explanation:

Simplify the equation.

`\begin{gathered} |x^2+2x-36|=12 \\ x^2+2x-36=\pm12 \end{gathered}`

Solve the x^2 + 2x - 36 = 12 for x.

`\begin{gathered} x^2+2x-36=12 \\ x^2+2x-36-12=0 \\ x^2+8x-6x-48=0 \\ x(x+8)-6(x-8)=0 \\ (x+8)(x-6)=0 \\ x=-8,6 \end{gathered}`

Solve the equation x^2 + 2x - 36 = -12 for x.

`\begin{gathered} x^2+2x-36+12=0 \\ x^2+2x-24=0 \\ x^2+6x-4x-24=0 \\ x(x+6)-4(x+6)=0 \\ (x+6)(x-4)=0 \\ x=-6,4 \end{gathered}`

Thus solution of the equation is x = -8, -6, 4, and 6