Question

Solve the equation using any method. Select the solution(s). -(x + 9)^2 = 64. POSSIBLE ANSWERS: A)x=-1 B) no real solution C) x=-(radical symbol here)1 D) x=(radical symbol here)1

Answer 1

B) no real solution

Step-by-step explanation

`-(x+9)^2=64`

Step 1

make

`(a+b)^2=a^2+2ab+b^2`

then

`-(x+9)^2=-(x^2-2\cdot9\cdot x+9^2)=-(x^2+18x+81)=-x^2-18x-81`

Hence

`\begin{gathered} -x^2-18x-81=64 \\ -x^2-18x-81-64=0 \\ -x^2-18x-145=0 \end{gathered}`

Step 2

find x, using the quadratic formula

`\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \end{gathered}`

Let

a=-1

b=-18

c=-145

replace,

`\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{+18\pm\sqrt[]{-18^2-4\cdot-1\cdot-145}}{2a} \\ x=\frac{-18\pm\sqrt[]{324-580}}{-2} \\ \\ x=\frac{-18\pm\sqrt[]{-256}}{-2} \\ \end{gathered}`

Now

`\sqrt[]{-256}`

is not a real number, so the answer is

B) no real solution