Solve -2left(x-19right)^2+13=0

$$-2 { \left(x-19 \right) }^{ 2 } +13=0$$

Solve for x

$$x=\frac{\sqrt{26}}{2}+19\approx 21.549509757$$

$$x=-\frac{\sqrt{26}}{2}+19\approx 16.450490243$$

Steps by Finding Square Root

Subtract 13 from both sides of the equation.

$$-2\left(x-19\right)^{2}+13-13=-13$$

Subtracting 13 from itself leaves 0.

$$-2\left(x-19\right)^{2}=-13$$

Divide both sides by -2.

$$\frac{-2\left(x-19\right)^{2}}{-2}=-\frac{13}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$\left(x-19\right)^{2}=-\frac{13}{-2}$$

Divide -13 by -2.

$$\left(x-19\right)^{2}=\frac{13}{2}$$

Take the square root of both sides of the equation.

$$x-19=\frac{\sqrt{26}}{2} x-19=-\frac{\sqrt{26}}{2}$$

Add 19 to both sides of the equation.

$$x-19-\left(-19\right)=\frac{\sqrt{26}}{2}-\left(-19\right) x-19-\left(-19\right)=-\frac{\sqrt{26}}{2}-\left(-19\right)$$

Subtracting -19 from itself leaves 0.

$$x=\frac{\sqrt{26}}{2}-\left(-19\right) x=-\frac{\sqrt{26}}{2}-\left(-19\right)$$

Subtract -19 from \frac{\sqrt{26}}{2}.

$$x=\frac{\sqrt{26}}{2}+19$$

Subtract -19 from -\frac{\sqrt{26}}{2}.

$$x=-\frac{\sqrt{26}}{2}+19$$

The equation is now solved.

$$x=\frac{\sqrt{26}}{2}+19 x=-\frac{\sqrt{26}}{2}+19$$