Solve x=sqrt{x^2+3x-21}

$$x = \sqrt { x ^ { 2 } + 3 x - 21 }$$

Solve for x

$$x=7$$

Solution Steps

Square both sides of the equation.

$$x^{2}=\left(\sqrt{x^{2}+3x-21}\right)^{2}$$

Calculate \sqrt{x^{2}+3x-21} to the power of 2 and get x^{2}+3x-21.

$$x^{2}=x^{2}+3x-21$$

Subtract x^{2} from both sides.

$$x^{2}-x^{2}=3x-21$$

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

$$0=3x-21$$

Swap sides so that all variable terms are on the left hand side.

$$3x-21=0$$

Add 21 to both sides. Anything plus zero gives itself.

$$3x=21$$

Divide both sides by 3.

$$x=\frac{21}{3}$$

Divide 21 by 3 to get 7.

$$x=7$$

Substitute 7 for x in the equation x=\sqrt{x^{2}+3x-21}.

$$7=\sqrt{7^{2}+3\times 7-21}$$

Simplify. The value x=7 satisfies the equation.

$$7=7$$

Equation x=\sqrt{x^{2}+3x-21} has a unique solution.

$$x=7$$