Solve 2x^2-5=20

$$2 { x }^{ 2 } -5=20$$

Solve for x

$$x = \frac{5 \sqrt{2}}{2} \approx 3.535533906$$

$$x = -\frac{5 \sqrt{2}}{2} \approx -3.535533906$$

Steps by Finding Square Root

Add 5 to both sides.

$$2x^{2}=20+5$$

Add 20 and 5 to get 25.

$$2x^{2}=25$$

Divide both sides by 2.

$$x^{2}=\frac{25}{2}$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Subtract 20 from both sides.

$$2x^{2}-5-20=0$$

Subtract 20 from -5 to get -25.

$$2x^{2}-25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-25\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-25\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-25\right)}}{2\times 2}$$

Multiply -8 times -25.

$$x=\frac{0±\sqrt{200}}{2\times 2}$$

Take the square root of 200.

$$x=\frac{0±10\sqrt{2}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±10\sqrt{2}}{4}$$

Now solve the equation x=\frac{0±10\sqrt{2}}{4} when ± is plus.

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

Now solve the equation x=\frac{0±10\sqrt{2}}{4} when ± is minus.

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

The equation is now solved.

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