Solve x^2/7+5=3

$$\frac { x ^ { 2 } } { 7 } + 5 = 3$$

Solve for x (complex solution)

$$x=-\sqrt{14}i\approx -0-3.741657387i$$

$$x=\sqrt{14}i\approx 3.741657387i$$

Steps by Finding Square Root

Multiply both sides of the equation by 7.

$$x^{2}+35=21$$

Subtract 35 from both sides.

$$x^{2}=21-35$$

Subtract 35 from 21 to get -14.

$$x^{2}=-14$$

The equation is now solved.

$$x=\sqrt{14}i x=-\sqrt{14}i$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 7.

$$x^{2}+35=21$$

Subtract 21 from both sides.

$$x^{2}+35-21=0$$

Subtract 21 from 35 to get 14.

$$x^{2}+14=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 14 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 14}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 14}}{2}$$

Multiply -4 times 14.

$$x=\frac{0±\sqrt{-56}}{2}$$

Take the square root of -56.

$$x=\frac{0±2\sqrt{14}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{14}i}{2} when ± is plus.

$$x=\sqrt{14}i$$

Now solve the equation x=\frac{0±2\sqrt{14}i}{2} when ± is minus.

$$x=-\sqrt{14}i$$

The equation is now solved.

$$x=\sqrt{14}i x=-\sqrt{14}i$$