Solve x^2+97=20

$$x ^ { 2 } + 97 = 20$$

Solve for x (complex solution)

$$x=-\sqrt{77}i\approx -0-8.774964387i$$

$$x=\sqrt{77}i\approx 8.774964387i$$

Steps by Finding Square Root

Subtract 97 from both sides.

$$x^{2}=20-97$$

Subtract 97 from 20 to get -77.

$$x^{2}=-77$$

The equation is now solved.

$$x=\sqrt{77}i x=-\sqrt{77}i$$

Steps Using the Quadratic Formula

Subtract 20 from both sides.

$$x^{2}+97-20=0$$

Subtract 20 from 97 to get 77.

$$x^{2}+77=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 77 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 77}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 77}}{2}$$

Multiply -4 times 77.

$$x=\frac{0±\sqrt{-308}}{2}$$

Take the square root of -308.

$$x=\frac{0±2\sqrt{77}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{77}i}{2} when ± is plus.

$$x=\sqrt{77}i$$

Now solve the equation x=\frac{0±2\sqrt{77}i}{2} when ± is minus.

$$x=-\sqrt{77}i$$

The equation is now solved.

$$x=\sqrt{77}i x=-\sqrt{77}i$$