Solve x^2+180^2=36

$$x ^ { 2 } + 180 ^ { 2 } = 36$$

Solve for x (complex solution)

$$x=-6\sqrt{899}i\approx -0-179.899972207i$$

$$x=6\sqrt{899}i\approx 179.899972207i$$

Steps by Finding Square Root

Calculate 180 to the power of 2 and get 32400.

$$x^{2}+32400=36$$

Subtract 32400 from both sides.

$$x^{2}=36-32400$$

Subtract 32400 from 36 to get -32364.

$$x^{2}=-32364$$

The equation is now solved.

$$x=6\sqrt{899}i x=-6\sqrt{899}i$$

Steps Using the Quadratic Formula

Calculate 180 to the power of 2 and get 32400.

$$x^{2}+32400=36$$

Subtract 36 from both sides.

$$x^{2}+32400-36=0$$

Subtract 36 from 32400 to get 32364.

$$x^{2}+32364=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 32364 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 32364}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 32364}}{2}$$

Multiply -4 times 32364.

$$x=\frac{0±\sqrt{-129456}}{2}$$

Take the square root of -129456.

$$x=\frac{0±12\sqrt{899}i}{2}$$

Now solve the equation x=\frac{0±12\sqrt{899}i}{2} when ± is plus.

$$x=6\sqrt{899}i$$

Now solve the equation x=\frac{0±12\sqrt{899}i}{2} when ± is minus.

$$x=-6\sqrt{899}i$$

The equation is now solved.

$$x=6\sqrt{899}i x=-6\sqrt{899}i$$