Solve -1/5(x-3)^2+5=18

$$- \frac { 1 } { 5 } ( x - 3 ) ^ { 2 } + 5 = 18$$

Solve for x (complex solution)

$$x=-\sqrt{65}i+3\approx 3-8.062257748i$$

$$x=3+\sqrt{65}i\approx 3+8.062257748i$$

Steps by Finding Square Root

Subtracting 5 from itself leaves 0.

$$-\frac{1}{5}\left(x-3\right)^{2}=18-5$$

Subtract 5 from 18.

$$-\frac{1}{5}\left(x-3\right)^{2}=13$$

Multiply both sides by -5.

$$\frac{-\frac{1}{5}\left(x-3\right)^{2}}{-\frac{1}{5}}=\frac{13}{-\frac{1}{5}}$$

Dividing by -\frac{1}{5} undoes the multiplication by -\frac{1}{5}.

$$\left(x-3\right)^{2}=\frac{13}{-\frac{1}{5}}$$

Divide 13 by -\frac{1}{5} by multiplying 13 by the reciprocal of -\frac{1}{5}.

$$\left(x-3\right)^{2}=-65$$

Take the square root of both sides of the equation.

$$x-3=\sqrt{65}i x-3=-\sqrt{65}i$$

Add 3 to both sides of the equation.

$$x-3-\left(-3\right)=\sqrt{65}i-\left(-3\right) x-3-\left(-3\right)=-\sqrt{65}i-\left(-3\right)$$

Subtracting -3 from itself leaves 0.

$$x=\sqrt{65}i-\left(-3\right) x=-\sqrt{65}i-\left(-3\right)$$

Subtract -3 from i\sqrt{65}.

$$x=3+\sqrt{65}i$$

Subtract -3 from -i\sqrt{65}.

$$x=-\sqrt{65}i+3$$

The equation is now solved.

$$x=3+\sqrt{65}i x=-\sqrt{65}i+3$$