Solve 5x^2-1=6

$$5 x ^ { 2 } - 1 = 6$$

Solve for x

$$x = \frac{\sqrt{35}}{5} \approx 1.183215957$$

$$x = -\frac{\sqrt{35}}{5} \approx -1.183215957$$

Steps by Finding Square Root

Add 1 to both sides.

$$5x^{2}=6+1$$

Add 6 and 1 to get 7.

$$5x^{2}=7$$

Divide both sides by 5.

$$x^{2}=\frac{7}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{35}}{5} x=-\frac{\sqrt{35}}{5}$$

Steps Using the Quadratic Formula

Subtract 6 from both sides.

$$5x^{2}-1-6=0$$

Subtract 6 from -1 to get -7.

$$5x^{2}-7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-7\right)}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-7\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-7\right)}}{2\times 5}$$

Multiply -20 times -7.

$$x=\frac{0±\sqrt{140}}{2\times 5}$$

Take the square root of 140.

$$x=\frac{0±2\sqrt{35}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±2\sqrt{35}}{10}$$

Now solve the equation x=\frac{0±2\sqrt{35}}{10} when ± is plus.

$$x=\frac{\sqrt{35}}{5}$$

Now solve the equation x=\frac{0±2\sqrt{35}}{10} when ± is minus.

$$x=-\frac{\sqrt{35}}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{35}}{5} x=-\frac{\sqrt{35}}{5}$$