Solve x^2+8^2=33

$${ x }^{ 2 } + { 8 }^{ 2 } =33$$

Solve for x (complex solution)

$$x=-\sqrt{31}i\approx -0-5.567764363i$$

$$x=\sqrt{31}i\approx 5.567764363i$$

Steps by Finding Square Root

Calculate 8 to the power of 2 and get 64.

$$x^{2}+64=33$$

Subtract 64 from both sides.

$$x^{2}=33-64$$

Subtract 64 from 33 to get -31.

$$x^{2}=-31$$

The equation is now solved.

$$x=\sqrt{31}i x=-\sqrt{31}i$$

Steps Using the Quadratic Formula

Calculate 8 to the power of 2 and get 64.

$$x^{2}+64=33$$

Subtract 33 from both sides.

$$x^{2}+64-33=0$$

Subtract 33 from 64 to get 31.

$$x^{2}+31=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 31 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 31}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 31}}{2}$$

Multiply -4 times 31.

$$x=\frac{0±\sqrt{-124}}{2}$$

Take the square root of -124.

$$x=\frac{0±2\sqrt{31}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{31}i}{2} when ± is plus.

$$x=\sqrt{31}i$$

Now solve the equation x=\frac{0±2\sqrt{31}i}{2} when ± is minus.

$$x=-\sqrt{31}i$$

The equation is now solved.

$$x=\sqrt{31}i x=-\sqrt{31}i$$