Solve 2y^2-5=0

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

Solve for y

$$y = \frac{\sqrt{10}}{2} \approx 1.58113883$$

$$y = -\frac{\sqrt{10}}{2} \approx -1.58113883$$

Steps by Finding Square Root

Add 5 to both sides. Anything plus zero gives itself.

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

Divide both sides by 2.

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

Take the square root of both sides of the equation.

$$y=\frac{\sqrt{10}}{2} y=-\frac{\sqrt{10}}{2}$$

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.

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

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

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

Square 0.

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

Multiply -4 times 2.

$$y=\frac{0±\sqrt{-8\left(-5\right)}}{2\times 2}$$

Multiply -8 times -5.

$$y=\frac{0±\sqrt{40}}{2\times 2}$$

Take the square root of 40.

$$y=\frac{0±2\sqrt{10}}{2\times 2}$$

Multiply 2 times 2.

$$y=\frac{0±2\sqrt{10}}{4}$$

Now solve the equation y=\frac{0±2\sqrt{10}}{4} when ± is plus.

$$y=\frac{\sqrt{10}}{2}$$

Now solve the equation y=\frac{0±2\sqrt{10}}{4} when ± is minus.

$$y=-\frac{\sqrt{10}}{2}$$

The equation is now solved.

$$y=\frac{\sqrt{10}}{2} y=-\frac{\sqrt{10}}{2}$$