Solve (x)=sqrt{x^2-15x+54}

$$( x ) = \sqrt { x ^ { 2 } - 15 x + 54 }$$

Solve for x

$$x = \frac{18}{5} = 3\frac{3}{5} = 3.6$$

Solution Steps

Square both sides of the equation.

$$x^{2}=\left(\sqrt{x^{2}-15x+54}\right)^{2}$$

Calculate \sqrt{x^{2}-15x+54} to the power of 2 and get x^{2}-15x+54.

$$x^{2}=x^{2}-15x+54$$

Subtract x^{2} from both sides.

$$x^{2}-x^{2}=-15x+54$$

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

$$0=-15x+54$$

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

$$-15x+54=0$$

Subtract 54 from both sides. Anything subtracted from zero gives its negation.

$$-15x=-54$$

Divide both sides by -15.

$$x=\frac{-54}{-15}$$

Reduce the fraction \frac{-54}{-15} to lowest terms by extracting and canceling out -3.

$$x=\frac{18}{5}$$

Substitute \frac{18}{5} for x in the equation x=\sqrt{x^{2}-15x+54}.

$$\frac{18}{5}=\sqrt{\left(\frac{18}{5}\right)^{2}-15\times \frac{18}{5}+54}$$

Simplify. The value x=\frac{18}{5} satisfies the equation.

$$\frac{18}{5}=\frac{18}{5}$$

Equation x=\sqrt{x^{2}-15x+54} has a unique solution.

$$x=\frac{18}{5}$$