Solve sqrt{8x^2+81}-3x=0

$$\sqrt { 8 x ^ { 2 } + 81 } - 3 x = 0$$

Solve for x

$$x=9$$

Solution Steps

Subtract -3x from both sides of the equation.

$$\sqrt{8x^{2}+81}=3x$$

Square both sides of the equation.

$$\left(\sqrt{8x^{2}+81}\right)^{2}=\left(3x\right)^{2}$$

Calculate \sqrt{8x^{2}+81} to the power of 2 and get 8x^{2}+81.

$$8x^{2}+81=\left(3x\right)^{2}$$

Expand \left(3x\right)^{2}.

$$8x^{2}+81=3^{2}x^{2}$$

Calculate 3 to the power of 2 and get 9.

$$8x^{2}+81=9x^{2}$$

Subtract 9x^{2} from both sides.

$$8x^{2}+81-9x^{2}=0$$

Combine 8x^{2} and -9x^{2} to get -x^{2}.

$$-x^{2}+81=0$$

Subtract 81 from both sides. Anything subtracted from zero gives its negation.

$$-x^{2}=-81$$

Divide both sides by -1.

$$x^{2}=\frac{-81}{-1}$$

Fraction \frac{-81}{-1} can be simplified to 81 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=81$$

Take the square root of both sides of the equation.

$$x=9 x=-9$$

Substitute 9 for x in the equation \sqrt{8x^{2}+81}-3x=0.

$$\sqrt{8\times 9^{2}+81}-3\times 9=0$$

Simplify. The value x=9 satisfies the equation.

$$0=0$$

Substitute -9 for x in the equation \sqrt{8x^{2}+81}-3x=0.

$$\sqrt{8\left(-9\right)^{2}+81}-3\left(-9\right)=0$$

Simplify. The value x=-9 does not satisfy the equation.

$$54=0$$

Equation \sqrt{8x^{2}+81}=3x has a unique solution.

$$x=9$$