Solve 85=2x^2-10

$$85 = 2 x ^ { 2 } - 10$$

Solve for x

$$x = \frac{\sqrt{190}}{2} \approx 6.892024376$$

$$x = -\frac{\sqrt{190}}{2} \approx -6.892024376$$

Steps by Finding Square Root

Swap sides so that all variable terms are on the left hand side.

$$2x^{2}-10=85$$

Add 10 to both sides.

$$2x^{2}=85+10$$

Add 85 and 10 to get 95.

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

Divide both sides by 2.

$$x^{2}=\frac{95}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{190}}{2} x=-\frac{\sqrt{190}}{2}$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$2x^{2}-10=85$$

Subtract 85 from both sides.

$$2x^{2}-10-85=0$$

Subtract 85 from -10 to get -95.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -95 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-95\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-95\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-95\right)}}{2\times 2}$$

Multiply -8 times -95.

$$x=\frac{0±\sqrt{760}}{2\times 2}$$

Take the square root of 760.

$$x=\frac{0±2\sqrt{190}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±2\sqrt{190}}{4}$$

Now solve the equation x=\frac{0±2\sqrt{190}}{4} when ± is plus.

$$x=\frac{\sqrt{190}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{190}}{4} when ± is minus.

$$x=-\frac{\sqrt{190}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{190}}{2} x=-\frac{\sqrt{190}}{2}$$