Solve 4x^2-200=-20

$$4 { x }^{ 2 } -200=-20$$

Solve for x

$$x=3\sqrt{5}\approx 6.708203932$$

$$x=-3\sqrt{5}\approx -6.708203932$$

Steps by Finding Square Root

Add 200 to both sides.

$$4x^{2}=-20+200$$

Add -20 and 200 to get 180.

$$4x^{2}=180$$

Divide both sides by 4.

$$x^{2}=\frac{180}{4}$$

Divide 180 by 4 to get 45.

$$x^{2}=45$$

Take the square root of both sides of the equation.

$$x=3\sqrt{5} x=-3\sqrt{5}$$

Steps Using the Quadratic Formula

Add 20 to both sides.

$$4x^{2}-200+20=0$$

Add -200 and 20 to get -180.

$$4x^{2}-180=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -180 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-180\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-180\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-180\right)}}{2\times 4}$$

Multiply -16 times -180.

$$x=\frac{0±\sqrt{2880}}{2\times 4}$$

Take the square root of 2880.

$$x=\frac{0±24\sqrt{5}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±24\sqrt{5}}{8}$$

Now solve the equation x=\frac{0±24\sqrt{5}}{8} when ± is plus.

$$x=3\sqrt{5}$$

Now solve the equation x=\frac{0±24\sqrt{5}}{8} when ± is minus.

$$x=-3\sqrt{5}$$

The equation is now solved.

$$x=3\sqrt{5} x=-3\sqrt{5}$$