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\frac{2\left(x+5\right)^{2}}{2}=\frac{17}{2}
Divide both sides by 2.
\left(x+5\right)^{2}=\frac{17}{2}
Dividing by 2 undoes the multiplication by 2.
x+5=\frac{\sqrt{34}}{2} x+5=-\frac{\sqrt{34}}{2}
Take the square root of both sides of the equation.
x+5-5=\frac{\sqrt{34}}{2}-5 x+5-5=-\frac{\sqrt{34}}{2}-5
Subtract 5 from both sides of the equation.
x=\frac{\sqrt{34}}{2}-5 x=-\frac{\sqrt{34}}{2}-5
Subtracting 5 from itself leaves 0.