Question

I need help with a problem with solving by square roots in quadratic equation.

Answer 1

To solve for x, first, we add 3 to the given equation:

$\begin{gathered} 2(x+5)^2-3+3=44+3, \\ 2(x+5)^2=47. \end{gathered}$

Dividing by 2, we get:

$(x+5)^2=\frac{47}{2}.$

Therefore:

$x+5=\pm\sqrt{\frac{47}{2}}.$

Finally, subtracting 5 we get:

$x=\pm\sqrt{\frac{47}{2}}-5.$

Answer:

$x=\operatorname{\pm}\sqrt{\frac{47}{2}}-5.$