Solve x^2+7^2=2

$$x ^ { 2 } + 7 ^ { 2 } = 2$$

Solve for x (complex solution)

$$x=-\sqrt{47}i\approx -0-6.8556546i$$

$$x=\sqrt{47}i\approx 6.8556546i$$

Steps by Finding Square Root

Calculate 7 to the power of 2 and get 49.

$$x^{2}+49=2$$

Subtract 49 from both sides.

$$x^{2}=2-49$$

Subtract 49 from 2 to get -47.

$$x^{2}=-47$$

The equation is now solved.

$$x=\sqrt{47}i x=-\sqrt{47}i$$

Steps Using the Quadratic Formula

Calculate 7 to the power of 2 and get 49.

$$x^{2}+49=2$$

Subtract 2 from both sides.

$$x^{2}+49-2=0$$

Subtract 2 from 49 to get 47.

$$x^{2}+47=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 47 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 47}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 47}}{2}$$

Multiply -4 times 47.

$$x=\frac{0±\sqrt{-188}}{2}$$

Take the square root of -188.

$$x=\frac{0±2\sqrt{47}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{47}i}{2} when ± is plus.

$$x=\sqrt{47}i$$

Now solve the equation x=\frac{0±2\sqrt{47}i}{2} when ± is minus.

$$x=-\sqrt{47}i$$

The equation is now solved.

$$x=\sqrt{47}i x=-\sqrt{47}i$$