Respuesta :

[tex]\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}[/tex]

Using quadratic formula:

[tex]\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}[/tex]

Therefore, the solutions are:

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

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