Solve x^2+7^2=3

$${ x }^{ 2 } + { 7 }^{ 2 } =3$$

Solve for x (complex solution)

$$x=-\sqrt{46}i\approx -0-6.782329983i$$

$$x=\sqrt{46}i\approx 6.782329983i$$

Steps by Finding Square Root

Calculate 7 to the power of 2 and get 49.

$$x^{2}+49=3$$

Subtract 49 from both sides.

$$x^{2}=3-49$$

Subtract 49 from 3 to get -46.

$$x^{2}=-46$$

The equation is now solved.

$$x=\sqrt{46}i x=-\sqrt{46}i$$

Steps Using the Quadratic Formula

Calculate 7 to the power of 2 and get 49.

$$x^{2}+49=3$$

Subtract 3 from both sides.

$$x^{2}+49-3=0$$

Subtract 3 from 49 to get 46.

$$x^{2}+46=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 46 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 46}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 46}}{2}$$

Multiply -4 times 46.

$$x=\frac{0±\sqrt{-184}}{2}$$

Take the square root of -184.

$$x=\frac{0±2\sqrt{46}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{46}i}{2} when ± is plus.

$$x=\sqrt{46}i$$

Now solve the equation x=\frac{0±2\sqrt{46}i}{2} when ± is minus.

$$x=-\sqrt{46}i$$

The equation is now solved.

$$x=\sqrt{46}i x=-\sqrt{46}i$$