Solve y^2=78Rightarrowx^2/5+y^2/5=1

$$y ^ { 2 } = 78 \Rightarrow \frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { 5 } = 1$$

Solve for y

$$y=\sqrt{78}\approx 8.831760866$$

$$y=-\sqrt{78}\approx -8.831760866$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$y=\sqrt{78} y=-\sqrt{78}$$

Steps Using the Quadratic Formula

Subtract 78 from both sides.

$$y^{2}-78=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -78 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-78\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-78\right)}}{2}$$

Multiply -4 times -78.

$$y=\frac{0±\sqrt{312}}{2}$$

Take the square root of 312.

$$y=\frac{0±2\sqrt{78}}{2}$$

Now solve the equation y=\frac{0±2\sqrt{78}}{2} when ± is plus.

$$y=\sqrt{78}$$

Now solve the equation y=\frac{0±2\sqrt{78}}{2} when ± is minus.

$$y=-\sqrt{78}$$

The equation is now solved.

$$y=\sqrt{78} y=-\sqrt{78}$$