Solve 5y^2-35=0

$$5 y ^ { 2 } - 35 = 0$$

Solve for y

$$y=\sqrt{7}\approx 2.645751311$$

$$y=-\sqrt{7}\approx -2.645751311$$

Steps by Finding Square Root

Add 35 to both sides. Anything plus zero gives itself.

$$5y^{2}=35$$

Divide both sides by 5.

$$y^{2}=\frac{35}{5}$$

Divide 35 by 5 to get 7.

$$y^{2}=7$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$5y^{2}-35=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -35 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 5\left(-35\right)}}{2\times 5}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 5\left(-35\right)}}{2\times 5}$$

Multiply -4 times 5.

$$y=\frac{0±\sqrt{-20\left(-35\right)}}{2\times 5}$$

Multiply -20 times -35.

$$y=\frac{0±\sqrt{700}}{2\times 5}$$

Take the square root of 700.

$$y=\frac{0±10\sqrt{7}}{2\times 5}$$

Multiply 2 times 5.

$$y=\frac{0±10\sqrt{7}}{10}$$

Now solve the equation y=\frac{0±10\sqrt{7}}{10} when ± is plus.

$$y=\sqrt{7}$$

Now solve the equation y=\frac{0±10\sqrt{7}}{10} when ± is minus.

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

The equation is now solved.

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