Solve 4=20-4x^2

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

Solve for x

$$x=2$$

$$x=-2$$

Steps by Finding Square Root

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

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

Subtract 20 from both sides.

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

Subtract 20 from 4 to get -16.

$$-4x^{2}=-16$$

Divide both sides by -4.

$$x^{2}=\frac{-16}{-4}$$

Divide -16 by -4 to get 4.

$$x^{2}=4$$

Take the square root of both sides of the equation.

$$x=2 x=-2$$

Steps Using the Quadratic Formula

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

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

Subtract 4 from both sides.

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

Subtract 4 from 20 to get 16.

$$16-4x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-4x^{2}+16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -4 for a, 0 for b, and 16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

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

Multiply -4 times -4.

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

Multiply 16 times 16.

$$x=\frac{0±\sqrt{256}}{2\left(-4\right)}$$

Take the square root of 256.

$$x=\frac{0±16}{2\left(-4\right)}$$

Multiply 2 times -4.

$$x=\frac{0±16}{-8}$$

Now solve the equation x=\frac{0±16}{-8} when ± is plus. Divide 16 by -8.

$$x=-2$$

Now solve the equation x=\frac{0±16}{-8} when ± is minus. Divide -16 by -8.

$$x=2$$

The equation is now solved.

$$x=-2 x=2$$