Solve x^2=4x+20

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

Solve for x

$$x=2\sqrt{6}+2\approx 6.898979486$$

$$x=2-2\sqrt{6}\approx -2.898979486$$

Steps Using the Quadratic Formula

Subtract 4x from both sides.

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

Subtract 20 from both sides.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -4 for b, and -20 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\left(-20\right)}}{2}$$

Square -4.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\left(-20\right)}}{2}$$

Multiply -4 times -20.

$$x=\frac{-\left(-4\right)±\sqrt{16+80}}{2}$$

Add 16 to 80.

$$x=\frac{-\left(-4\right)±\sqrt{96}}{2}$$

Take the square root of 96.

$$x=\frac{-\left(-4\right)±4\sqrt{6}}{2}$$

The opposite of -4 is 4.

$$x=\frac{4±4\sqrt{6}}{2}$$

Now solve the equation x=\frac{4±4\sqrt{6}}{2} when ± is plus. Add 4 to 4\sqrt{6}.

$$x=\frac{4\sqrt{6}+4}{2}$$

Divide 4+4\sqrt{6} by 2.

$$x=2\sqrt{6}+2$$

Now solve the equation x=\frac{4±4\sqrt{6}}{2} when ± is minus. Subtract 4\sqrt{6} from 4.

$$x=\frac{4-4\sqrt{6}}{2}$$

Divide 4-4\sqrt{6} by 2.

$$x=2-2\sqrt{6}$$

The equation is now solved.

$$x=2\sqrt{6}+2 x=2-2\sqrt{6}$$

Steps for Completing the Square

Subtract 4x from both sides.

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

Divide -4, the coefficient of the x term, by 2 to get -2. Then add the square of -2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-4x+\left(-2\right)^{2}=20+\left(-2\right)^{2}$$

Square -2.

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

Add 20 to 4.

$$x^{2}-4x+4=24$$

Factor x^{2}-4x+4. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-2\right)^{2}=24$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{24}$$

Simplify.

$$x-2=2\sqrt{6} x-2=-2\sqrt{6}$$

Add 2 to both sides of the equation.

$$x=2\sqrt{6}+2 x=2-2\sqrt{6}$$