Solve 2r^2-1=0

$$2 r ^ { 2 } - 1 = 0$$

Solve for r

$$r=\frac{\sqrt{2}}{2}\approx 0.707106781$$

$$r=-\frac{\sqrt{2}}{2}\approx -0.707106781$$

Steps by Finding Square Root

Add 1 to both sides. Anything plus zero gives itself.

$$2r^{2}=1$$

Divide both sides by 2.

$$r^{2}=\frac{1}{2}$$

Take the square root of both sides of the equation.

$$r=\frac{\sqrt{2}}{2} r=-\frac{\sqrt{2}}{2}$$

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.

$$2r^{2}-1=0$$

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

$$r=\frac{0±\sqrt{0^{2}-4\times 2\left(-1\right)}}{2\times 2}$$

Square 0.

$$r=\frac{0±\sqrt{-4\times 2\left(-1\right)}}{2\times 2}$$

Multiply -4 times 2.

$$r=\frac{0±\sqrt{-8\left(-1\right)}}{2\times 2}$$

Multiply -8 times -1.

$$r=\frac{0±\sqrt{8}}{2\times 2}$$

Take the square root of 8.

$$r=\frac{0±2\sqrt{2}}{2\times 2}$$

Multiply 2 times 2.

$$r=\frac{0±2\sqrt{2}}{4}$$

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

$$r=\frac{\sqrt{2}}{2}$$

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

$$r=-\frac{\sqrt{2}}{2}$$

The equation is now solved.

$$r=\frac{\sqrt{2}}{2} r=-\frac{\sqrt{2}}{2}$$