Solve (x)=sqrt{4x-20}

$$( x ) = \sqrt { 4 x - 20 }$$

Solve for x (complex solution)

$$x=2-4i$$

$$x=2+4i$$

Solution Steps

Square both sides of the equation.

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

Calculate \sqrt{4x-20} to the power of 2 and get 4x-20.

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

Subtract 4x from both sides.

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

Add 20 to 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}.

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

Square -4.

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

Multiply -4 times 20.

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

Add 16 to -80.

$$x=\frac{-\left(-4\right)±\sqrt{-64}}{2}$$

Take the square root of -64.

$$x=\frac{-\left(-4\right)±8i}{2}$$

The opposite of -4 is 4.

$$x=\frac{4±8i}{2}$$

Now solve the equation x=\frac{4±8i}{2} when ± is plus. Add 4 to 8i.

$$x=\frac{4+8i}{2}$$

Divide 4+8i by 2.

$$x=2+4i$$

Now solve the equation x=\frac{4±8i}{2} when ± is minus. Subtract 8i from 4.

$$x=\frac{4-8i}{2}$$

Divide 4-8i by 2.

$$x=2-4i$$

The equation is now solved.

$$x=2+4i x=2-4i$$

Substitute 2+4i for x in the equation x=\sqrt{4x-20}.

$$2+4i=\sqrt{4\left(2+4i\right)-20}$$

Simplify. The value x=2+4i satisfies the equation.

$$2+4i=2+4i$$

Substitute 2-4i for x in the equation x=\sqrt{4x-20}.

$$2-4i=\sqrt{4\left(2-4i\right)-20}$$

Simplify. The value x=2-4i satisfies the equation.

$$2-4i=2-4i$$

List all solutions of x=\sqrt{4x-20}.

$$x=2+4i x=2-4i$$