Solve (x-4)^2=-5

$$( x - 4 ) ^ { 2 } = - 5$$

Solve for x (complex solution)

$$x=-\sqrt{5}i+4\approx 4-2.236067977i$$

$$x=4+\sqrt{5}i\approx 4+2.236067977i$$

Steps by Finding Square Root

Add 4 to both sides of the equation.

$$x-4-\left(-4\right)=\sqrt{5}i-\left(-4\right) x-4-\left(-4\right)=-\sqrt{5}i-\left(-4\right)$$

Subtracting -4 from itself leaves 0.

$$x=\sqrt{5}i-\left(-4\right) x=-\sqrt{5}i-\left(-4\right)$$

Subtract -4 from i\sqrt{5}.

$$x=4+\sqrt{5}i$$

Subtract -4 from -i\sqrt{5}.

$$x=-\sqrt{5}i+4$$

The equation is now solved.

$$x=4+\sqrt{5}i x=-\sqrt{5}i+4$$