Question

What are the solutions of 4(x+6)^2=52 select two answers A) √13 - 6B) -19 C) -√13-6D)-2√13-6E)2√13-6

Answer 1

`\begin{gathered} 4(x+6)^2=52 \\ \text{Divide both sides by 4:} \\ (x+6)^2=13 \\ \text{Expand the left hand side:} \\ x^2+12x+36=13 \\ \text{Subtract 13 from both sides:} \\ x^2+12x+23=0 \\ \text{ } \end{gathered}`

Using quadratic formula:

`\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-12\pm\sqrt[]{144-4(1)(23)}}{2} \\ x=\frac{-12\pm\sqrt[]{52}}{2} \\ x=-6\pm\sqrt[]{13} \end{gathered}`

Therefore, the solutions are:

`\begin{gathered} x=\sqrt[]{13}-6 \\ or \\ x=-\sqrt[]{13}-6 \end{gathered}`