Solve 8sqrt{3^2}=x^2+2x^2

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

Solve for x

$$x=2\sqrt{2}\approx 2.828427125$$

$$x=-2\sqrt{2}\approx -2.828427125$$

Steps by Finding Square Root

Calculate 3 to the power of 2 and get 9.

$$8\sqrt{9}=x^{2}+2x^{2}$$

Calculate the square root of 9 and get 3.

$$8\times 3=x^{2}+2x^{2}$$

Multiply 8 and 3 to get 24.

$$24=x^{2}+2x^{2}$$

Combine x^{2} and 2x^{2} to get 3x^{2}.

$$24=3x^{2}$$

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

$$3x^{2}=24$$

Divide both sides by 3.

$$x^{2}=\frac{24}{3}$$

Divide 24 by 3 to get 8.

$$x^{2}=8$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Calculate 3 to the power of 2 and get 9.

$$8\sqrt{9}=x^{2}+2x^{2}$$

Calculate the square root of 9 and get 3.

$$8\times 3=x^{2}+2x^{2}$$

Multiply 8 and 3 to get 24.

$$24=x^{2}+2x^{2}$$

Combine x^{2} and 2x^{2} to get 3x^{2}.

$$24=3x^{2}$$

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

$$3x^{2}=24$$

Subtract 24 from both sides.

$$3x^{2}-24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-24\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-24\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-24\right)}}{2\times 3}$$

Multiply -12 times -24.

$$x=\frac{0±\sqrt{288}}{2\times 3}$$

Take the square root of 288.

$$x=\frac{0±12\sqrt{2}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±12\sqrt{2}}{6}$$

Now solve the equation x=\frac{0±12\sqrt{2}}{6} when ± is plus.

$$x=2\sqrt{2}$$

Now solve the equation x=\frac{0±12\sqrt{2}}{6} when ± is minus.

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

The equation is now solved.

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