Solve x-2=sqrt{8x-48}

$$x-2= \sqrt{ 8x-48 }$$

Solve for x (complex solution)

$$x=6+4i$$

$$x=6-4i$$

Solution Steps

Square both sides of the equation.

$$\left(x-2\right)^{2}=\left(\sqrt{8x-48}\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.

$$x^{2}-4x+4=\left(\sqrt{8x-48}\right)^{2}$$

Calculate \sqrt{8x-48} to the power of 2 and get 8x-48.

$$x^{2}-4x+4=8x-48$$

Subtract 8x from both sides.

$$x^{2}-4x+4-8x=-48$$

Combine -4x and -8x to get -12x.

$$x^{2}-12x+4=-48$$

Add 48 to both sides.

$$x^{2}-12x+4+48=0$$

Add 4 and 48 to get 52.

$$x^{2}-12x+52=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -12 for b, and 52 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 52}}{2}$$

Square -12.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\times 52}}{2}$$

Multiply -4 times 52.

$$x=\frac{-\left(-12\right)±\sqrt{144-208}}{2}$$

Add 144 to -208.

$$x=\frac{-\left(-12\right)±\sqrt{-64}}{2}$$

Take the square root of -64.

$$x=\frac{-\left(-12\right)±8i}{2}$$

The opposite of -12 is 12.

$$x=\frac{12±8i}{2}$$

Now solve the equation x=\frac{12±8i}{2} when ± is plus. Add 12 to 8i.

$$x=\frac{12+8i}{2}$$

Divide 12+8i by 2.

$$x=6+4i$$

Now solve the equation x=\frac{12±8i}{2} when ± is minus. Subtract 8i from 12.

$$x=\frac{12-8i}{2}$$

Divide 12-8i by 2.

$$x=6-4i$$

The equation is now solved.

$$x=6+4i x=6-4i$$

Substitute 6+4i for x in the equation x-2=\sqrt{8x-48}.

$$6+4i-2=\sqrt{8\left(6+4i\right)-48}$$

Simplify. The value x=6+4i satisfies the equation.

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

Substitute 6-4i for x in the equation x-2=\sqrt{8x-48}.

$$6-4i-2=\sqrt{8\left(6-4i\right)-48}$$

Simplify. The value x=6-4i satisfies the equation.

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

List all solutions of x-2=\sqrt{8x-48}.

$$x=6+4i x=6-4i$$