Solve 5x^2-2=1

$$5 x ^ { 2 } - 2 = 1$$

Solve for x

$$x=\frac{\sqrt{15}}{5}\approx 0.774596669$$

$$x=-\frac{\sqrt{15}}{5}\approx -0.774596669$$

Steps by Finding Square Root

Add 2 to both sides.

$$5x^{2}=1+2$$

Add 1 and 2 to get 3.

$$5x^{2}=3$$

Divide both sides by 5.

$$x^{2}=\frac{3}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{15}}{5} x=-\frac{\sqrt{15}}{5}$$

Steps Using the Quadratic Formula

Subtract 1 from both sides.

$$5x^{2}-2-1=0$$

Subtract 1 from -2 to get -3.

$$5x^{2}-3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-3\right)}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-3\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-3\right)}}{2\times 5}$$

Multiply -20 times -3.

$$x=\frac{0±\sqrt{60}}{2\times 5}$$

Take the square root of 60.

$$x=\frac{0±2\sqrt{15}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±2\sqrt{15}}{10}$$

Now solve the equation x=\frac{0±2\sqrt{15}}{10} when ± is plus.

$$x=\frac{\sqrt{15}}{5}$$

Now solve the equation x=\frac{0±2\sqrt{15}}{10} when ± is minus.

$$x=-\frac{\sqrt{15}}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{15}}{5} x=-\frac{\sqrt{15}}{5}$$