Solve 2x^2-10=30

$$2 x ^ { 2 } - 10 = 30$$

Solve for x

$$x=2\sqrt{5}\approx 4.472135955$$

$$x=-2\sqrt{5}\approx -4.472135955$$

Steps by Finding Square Root

Add 10 to both sides.

$$2x^{2}=30+10$$

Add 30 and 10 to get 40.

$$2x^{2}=40$$

Divide both sides by 2.

$$x^{2}=\frac{40}{2}$$

Divide 40 by 2 to get 20.

$$x^{2}=20$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Subtract 30 from both sides.

$$2x^{2}-10-30=0$$

Subtract 30 from -10 to get -40.

$$2x^{2}-40=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -40 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-40\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-40\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-40\right)}}{2\times 2}$$

Multiply -8 times -40.

$$x=\frac{0±\sqrt{320}}{2\times 2}$$

Take the square root of 320.

$$x=\frac{0±8\sqrt{5}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±8\sqrt{5}}{4}$$

Now solve the equation x=\frac{0±8\sqrt{5}}{4} when ± is plus.

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

Now solve the equation x=\frac{0±8\sqrt{5}}{4} when ± is minus.

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

The equation is now solved.

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