Solve 7y^2-7=93

$$7 y ^ { 2 } - 7 = 93$$

Solve for y

$$y = \frac{10 \sqrt{7}}{7} \approx 3.77964473$$

$$y = -\frac{10 \sqrt{7}}{7} \approx -3.77964473$$

Steps by Finding Square Root

Add 7 to both sides.

$$7y^{2}=93+7$$

Add 93 and 7 to get 100.

$$7y^{2}=100$$

Divide both sides by 7.

$$y^{2}=\frac{100}{7}$$

Take the square root of both sides of the equation.

$$y=\frac{10\sqrt{7}}{7} y=-\frac{10\sqrt{7}}{7}$$

Steps Using the Quadratic Formula

Subtract 93 from both sides.

$$7y^{2}-7-93=0$$

Subtract 93 from -7 to get -100.

$$7y^{2}-100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, 0 for b, and -100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 7\left(-100\right)}}{2\times 7}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 7\left(-100\right)}}{2\times 7}$$

Multiply -4 times 7.

$$y=\frac{0±\sqrt{-28\left(-100\right)}}{2\times 7}$$

Multiply -28 times -100.

$$y=\frac{0±\sqrt{2800}}{2\times 7}$$

Take the square root of 2800.

$$y=\frac{0±20\sqrt{7}}{2\times 7}$$

Multiply 2 times 7.

$$y=\frac{0±20\sqrt{7}}{14}$$

Now solve the equation y=\frac{0±20\sqrt{7}}{14} when ± is plus.

$$y=\frac{10\sqrt{7}}{7}$$

Now solve the equation y=\frac{0±20\sqrt{7}}{14} when ± is minus.

$$y=-\frac{10\sqrt{7}}{7}$$

The equation is now solved.

$$y=\frac{10\sqrt{7}}{7} y=-\frac{10\sqrt{7}}{7}$$