Solve 2x^2+20=95

$$2 x ^ { 2 } + 20 = 95$$

Solve for x

$$x = \frac{5 \sqrt{6}}{2} \approx 6.123724357$$

$$x = -\frac{5 \sqrt{6}}{2} \approx -6.123724357$$

Steps by Finding Square Root

Subtract 20 from both sides.

$$2x^{2}=95-20$$

Subtract 20 from 95 to get 75.

$$2x^{2}=75$$

Divide both sides by 2.

$$x^{2}=\frac{75}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{5\sqrt{6}}{2} x=-\frac{5\sqrt{6}}{2}$$

Steps Using the Quadratic Formula

Subtract 95 from both sides.

$$2x^{2}+20-95=0$$

Subtract 95 from 20 to get -75.

$$2x^{2}-75=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -75 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-75\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-75\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-75\right)}}{2\times 2}$$

Multiply -8 times -75.

$$x=\frac{0±\sqrt{600}}{2\times 2}$$

Take the square root of 600.

$$x=\frac{0±10\sqrt{6}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±10\sqrt{6}}{4}$$

Now solve the equation x=\frac{0±10\sqrt{6}}{4} when ± is plus.

$$x=\frac{5\sqrt{6}}{2}$$

Now solve the equation x=\frac{0±10\sqrt{6}}{4} when ± is minus.

$$x=-\frac{5\sqrt{6}}{2}$$

The equation is now solved.

$$x=\frac{5\sqrt{6}}{2} x=-\frac{5\sqrt{6}}{2}$$