Solve 7y^2+3yy+28=0

$$7 y ^ { 2 } + 3 y y + 28 = 0$$

Solve for y

$$y=-\frac{\sqrt{70}i}{5}\approx -0-1.673320053i$$

$$y=\frac{\sqrt{70}i}{5}\approx 1.673320053i$$

Steps by Finding Square Root

Multiply y and y to get y^{2}.

$$7y^{2}+3y^{2}+28=0$$

Combine 7y^{2} and 3y^{2} to get 10y^{2}.

$$10y^{2}+28=0$$

Subtract 28 from both sides. Anything subtracted from zero gives its negation.

$$10y^{2}=-28$$

Divide both sides by 10.

$$y^{2}=\frac{-28}{10}$$

Reduce the fraction \frac{-28}{10} to lowest terms by extracting and canceling out 2.

$$y^{2}=-\frac{14}{5}$$

The equation is now solved.

$$y=\frac{\sqrt{70}i}{5} y=-\frac{\sqrt{70}i}{5}$$

Steps Using the Quadratic Formula

Multiply y and y to get y^{2}.

$$7y^{2}+3y^{2}+28=0$$

Combine 7y^{2} and 3y^{2} to get 10y^{2}.

$$10y^{2}+28=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 10 for a, 0 for b, and 28 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 10\times 28}}{2\times 10}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 10\times 28}}{2\times 10}$$

Multiply -4 times 10.

$$y=\frac{0±\sqrt{-40\times 28}}{2\times 10}$$

Multiply -40 times 28.

$$y=\frac{0±\sqrt{-1120}}{2\times 10}$$

Take the square root of -1120.

$$y=\frac{0±4\sqrt{70}i}{2\times 10}$$

Multiply 2 times 10.

$$y=\frac{0±4\sqrt{70}i}{20}$$

Now solve the equation y=\frac{0±4\sqrt{70}i}{20} when ± is plus.

$$y=\frac{\sqrt{70}i}{5}$$

Now solve the equation y=\frac{0±4\sqrt{70}i}{20} when ± is minus.

$$y=-\frac{\sqrt{70}i}{5}$$

The equation is now solved.

$$y=\frac{\sqrt{70}i}{5} y=-\frac{\sqrt{70}i}{5}$$