Solve y^2=7/8(132/47)-9/2

$${ y }^{ 2 } = \frac{ 7 }{ 8 } ( \frac{ 132 }{ 47 } )- \frac{ 9 }{ 2 }$$

Solve for y

$$y=-\frac{4\sqrt{282}i}{47}\approx -0-1.429179202i$$

$$y=\frac{4\sqrt{282}i}{47}\approx 1.429179202i$$

Steps by Finding Square Root

Multiply \frac{7}{8} and \frac{132}{47} to get \frac{231}{94}.

$$y^{2}=\frac{231}{94}-\frac{9}{2}$$

Subtract \frac{9}{2} from \frac{231}{94} to get -\frac{96}{47}.

$$y^{2}=-\frac{96}{47}$$

The equation is now solved.

$$y=\frac{4\sqrt{282}i}{47} y=-\frac{4\sqrt{282}i}{47}$$

Steps Using the Quadratic Formula

Multiply \frac{7}{8} and \frac{132}{47} to get \frac{231}{94}.

$$y^{2}=\frac{231}{94}-\frac{9}{2}$$

Subtract \frac{9}{2} from \frac{231}{94} to get -\frac{96}{47}.

$$y^{2}=-\frac{96}{47}$$

Add \frac{96}{47} to both sides.

$$y^{2}+\frac{96}{47}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and \frac{96}{47} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times \frac{96}{47}}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times \frac{96}{47}}}{2}$$

Multiply -4 times \frac{96}{47}.

$$y=\frac{0±\sqrt{-\frac{384}{47}}}{2}$$

Take the square root of -\frac{384}{47}.

$$y=\frac{0±\frac{8\sqrt{282}i}{47}}{2}$$

Now solve the equation y=\frac{0±\frac{8\sqrt{282}i}{47}}{2} when ± is plus.

$$y=\frac{4\sqrt{282}i}{47}$$

Now solve the equation y=\frac{0±\frac{8\sqrt{282}i}{47}}{2} when ± is minus.

$$y=-\frac{4\sqrt{282}i}{47}$$

The equation is now solved.

$$y=\frac{4\sqrt{282}i}{47} y=-\frac{4\sqrt{282}i}{47}$$