Solve 7y^2+18=4

$$7 { y }^{ 2 } +18=4$$

Solve for y

$$y=-\sqrt{2}i\approx -0-1.414213562i$$

$$y=\sqrt{2}i\approx 1.414213562i$$

Steps by Finding Square Root

Subtract 18 from both sides.

$$7y^{2}=4-18$$

Subtract 18 from 4 to get -14.

$$7y^{2}=-14$$

Divide both sides by 7.

$$y^{2}=\frac{-14}{7}$$

Divide -14 by 7 to get -2.

$$y^{2}=-2$$

The equation is now solved.

$$y=\sqrt{2}i y=-\sqrt{2}i$$

Steps Using the Quadratic Formula

Subtract 4 from both sides.

$$7y^{2}+18-4=0$$

Subtract 4 from 18 to get 14.

$$7y^{2}+14=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, 0 for b, and 14 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 7\times 14}}{2\times 7}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 7\times 14}}{2\times 7}$$

Multiply -4 times 7.

$$y=\frac{0±\sqrt{-28\times 14}}{2\times 7}$$

Multiply -28 times 14.

$$y=\frac{0±\sqrt{-392}}{2\times 7}$$

Take the square root of -392.

$$y=\frac{0±14\sqrt{2}i}{2\times 7}$$

Multiply 2 times 7.

$$y=\frac{0±14\sqrt{2}i}{14}$$

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

$$y=\sqrt{2}i$$

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

$$y=-\sqrt{2}i$$

The equation is now solved.

$$y=\sqrt{2}i y=-\sqrt{2}i$$