Solve sqrt{x^2-5x+10}=x

$$\sqrt { x ^ { 2 } - 5 x + 10 } = x$$

Solve for x

$$x=2$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{x^{2}-5x+10}\right)^{2}=x^{2}$$

Calculate \sqrt{x^{2}-5x+10} to the power of 2 and get x^{2}-5x+10.

$$x^{2}-5x+10=x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}-5x+10-x^{2}=0$$

Combine x^{2} and -x^{2} to get 0.

$$-5x+10=0$$

Subtract 10 from both sides. Anything subtracted from zero gives its negation.

$$-5x=-10$$

Divide both sides by -5.

$$x=\frac{-10}{-5}$$

Divide -10 by -5 to get 2.

$$x=2$$

Substitute 2 for x in the equation \sqrt{x^{2}-5x+10}=x.

$$\sqrt{2^{2}-5\times 2+10}=2$$

Simplify. The value x=2 satisfies the equation.

$$2=2$$

Equation \sqrt{x^{2}-5x+10}=x has a unique solution.

$$x=2$$