Solve 3=7x^2-4(-7)+21

$$3 = 7 x ^ { 2 } - 4 ( - 7 ) + 21$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{322}i}{7}\approx -0-2.563479778i$$

$$x=\frac{\sqrt{322}i}{7}\approx 2.563479778i$$

Steps by Finding Square Root

Multiply 4 and -7 to get -28.

$$3=7x^{2}-\left(-28\right)+21$$

The opposite of -28 is 28.

$$3=7x^{2}+28+21$$

Add 28 and 21 to get 49.

$$3=7x^{2}+49$$

Swap sides so that all variable terms are on the left hand side.

$$7x^{2}+49=3$$

Subtract 49 from both sides.

$$7x^{2}=3-49$$

Subtract 49 from 3 to get -46.

$$7x^{2}=-46$$

Divide both sides by 7.

$$x^{2}=-\frac{46}{7}$$

The equation is now solved.

$$x=\frac{\sqrt{322}i}{7} x=-\frac{\sqrt{322}i}{7}$$

Steps Using the Quadratic Formula

Multiply 4 and -7 to get -28.

$$3=7x^{2}-\left(-28\right)+21$$

The opposite of -28 is 28.

$$3=7x^{2}+28+21$$

Add 28 and 21 to get 49.

$$3=7x^{2}+49$$

Swap sides so that all variable terms are on the left hand side.

$$7x^{2}+49=3$$

Subtract 3 from both sides.

$$7x^{2}+49-3=0$$

Subtract 3 from 49 to get 46.

$$7x^{2}+46=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, 0 for b, and 46 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 7\times 46}}{2\times 7}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 7\times 46}}{2\times 7}$$

Multiply -4 times 7.

$$x=\frac{0±\sqrt{-28\times 46}}{2\times 7}$$

Multiply -28 times 46.

$$x=\frac{0±\sqrt{-1288}}{2\times 7}$$

Take the square root of -1288.

$$x=\frac{0±2\sqrt{322}i}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{0±2\sqrt{322}i}{14}$$

Now solve the equation x=\frac{0±2\sqrt{322}i}{14} when ± is plus.

$$x=\frac{\sqrt{322}i}{7}$$

Now solve the equation x=\frac{0±2\sqrt{322}i}{14} when ± is minus.

$$x=-\frac{\sqrt{322}i}{7}$$

The equation is now solved.

$$x=\frac{\sqrt{322}i}{7} x=-\frac{\sqrt{322}i}{7}$$