Solve 2+sqrt{8-4x}=x

$$2 + \sqrt { 8 - 4 x } = x$$

Solve for x

$$x=2$$

Solution Steps

Subtract 2 from both sides of the equation.

$$\sqrt{8-4x}=x-2$$

Square both sides of the equation.

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

Calculate \sqrt{8-4x} to the power of 2 and get 8-4x.

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

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

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

Subtract x^{2} from both sides.

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

Add 4x to both sides.

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

Combine -4x and 4x to get 0.

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

Subtract 8 from both sides.

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

Subtract 8 from 4 to get -4.

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

Divide both sides by -1.

$$x^{2}=\frac{-4}{-1}$$

Fraction \frac{-4}{-1} can be simplified to 4 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=4$$

Take the square root of both sides of the equation.

$$x=2 x=-2$$

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

$$2+\sqrt{8-4\times 2}=2$$

Simplify. The value x=2 satisfies the equation.

$$2=2$$

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

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

Simplify. The value x=-2 does not satisfy the equation because the left and the right hand side have opposite signs.

$$6=-2$$

Equation \sqrt{8-4x}=x-2 has a unique solution.

$$x=2$$