Solve 59y^2=18

$$59 y ^ { 2 } = 18$$

Solve for y

$$y=\frac{3\sqrt{118}}{59}\approx 0.552344771$$

$$y=-\frac{3\sqrt{118}}{59}\approx -0.552344771$$

Steps by Finding Square Root

Divide both sides by 59.

$$y^{2}=\frac{18}{59}$$

Take the square root of both sides of the equation.

$$y=\frac{3\sqrt{118}}{59} y=-\frac{3\sqrt{118}}{59}$$

Steps Using the Quadratic Formula

Divide both sides by 59.

$$y^{2}=\frac{18}{59}$$

Subtract \frac{18}{59} from both sides.

$$y^{2}-\frac{18}{59}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{18}{59} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-\frac{18}{59}\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-\frac{18}{59}\right)}}{2}$$

Multiply -4 times -\frac{18}{59}.

$$y=\frac{0±\sqrt{\frac{72}{59}}}{2}$$

Take the square root of \frac{72}{59}.

$$y=\frac{0±\frac{6\sqrt{118}}{59}}{2}$$

Now solve the equation y=\frac{0±\frac{6\sqrt{118}}{59}}{2} when ± is plus.

$$y=\frac{3\sqrt{118}}{59}$$

Now solve the equation y=\frac{0±\frac{6\sqrt{118}}{59}}{2} when ± is minus.

$$y=-\frac{3\sqrt{118}}{59}$$

The equation is now solved.

$$y=\frac{3\sqrt{118}}{59} y=-\frac{3\sqrt{118}}{59}$$