Solve 2x^2=left(10+8+6right)^2

$$2 { x }^{ 2 } = { \left(10+8+6 \right) }^{ 2 }$$

Solve for x

$$x=12\sqrt{2}\approx 16.970562748$$

$$x=-12\sqrt{2}\approx -16.970562748$$

Steps by Finding Square Root

Add 10 and 8 to get 18.

$$2x^{2}=\left(18+6\right)^{2}$$

Add 18 and 6 to get 24.

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

Calculate 24 to the power of 2 and get 576.

$$2x^{2}=576$$

Divide both sides by 2.

$$x^{2}=\frac{576}{2}$$

Divide 576 by 2 to get 288.

$$x^{2}=288$$

Take the square root of both sides of the equation.

$$x=12\sqrt{2} x=-12\sqrt{2}$$

Steps Using the Quadratic Formula

Add 10 and 8 to get 18.

$$2x^{2}=\left(18+6\right)^{2}$$

Add 18 and 6 to get 24.

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

Calculate 24 to the power of 2 and get 576.

$$2x^{2}=576$$

Subtract 576 from both sides.

$$2x^{2}-576=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -576 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-576\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-576\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-576\right)}}{2\times 2}$$

Multiply -8 times -576.

$$x=\frac{0±\sqrt{4608}}{2\times 2}$$

Take the square root of 4608.

$$x=\frac{0±48\sqrt{2}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±48\sqrt{2}}{4}$$

Now solve the equation x=\frac{0±48\sqrt{2}}{4} when ± is plus.

$$x=12\sqrt{2}$$

Now solve the equation x=\frac{0±48\sqrt{2}}{4} when ± is minus.

$$x=-12\sqrt{2}$$

The equation is now solved.

$$x=12\sqrt{2} x=-12\sqrt{2}$$