Solve x^2=144+128-2*8sqrt{2}*12*07

$${ x }^{ 2 } =144+128-2 \times 8 \sqrt{ 2 } \times 12 \times 07$$

Solve for x

$$x=4\sqrt{17}\approx 16.492422502$$

$$x=-4\sqrt{17}\approx -16.492422502$$

Steps by Finding Square Root

Add 144 and 128 to get 272.

$$x^{2}=272-0\times 2\times 7\times 8\times 12\sqrt{2}$$

Multiply 0 and 2 to get 0.

$$x^{2}=272-0\times 7\times 8\times 12\sqrt{2}$$

Multiply 0 and 7 to get 0.

$$x^{2}=272-0\times 8\times 12\sqrt{2}$$

Multiply 0 and 8 to get 0.

$$x^{2}=272-0\times 12\sqrt{2}$$

Multiply 0 and 12 to get 0.

$$x^{2}=272-0\sqrt{2}$$

Anything times zero gives zero.

$$x^{2}=272-0$$

Subtract 0 from 272 to get 272.

$$x^{2}=272$$

Take the square root of both sides of the equation.

$$x=4\sqrt{17} x=-4\sqrt{17}$$

Steps Using the Quadratic Formula

Add 144 and 128 to get 272.

$$x^{2}=272-0\times 2\times 7\times 8\times 12\sqrt{2}$$

Multiply 0 and 2 to get 0.

$$x^{2}=272-0\times 7\times 8\times 12\sqrt{2}$$

Multiply 0 and 7 to get 0.

$$x^{2}=272-0\times 8\times 12\sqrt{2}$$

Multiply 0 and 8 to get 0.

$$x^{2}=272-0\times 12\sqrt{2}$$

Multiply 0 and 12 to get 0.

$$x^{2}=272-0\sqrt{2}$$

Anything times zero gives zero.

$$x^{2}=272-0$$

Subtract 0 from 272 to get 272.

$$x^{2}=272$$

Subtract 272 from both sides.

$$x^{2}-272=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -272 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-272\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-272\right)}}{2}$$

Multiply -4 times -272.

$$x=\frac{0±\sqrt{1088}}{2}$$

Take the square root of 1088.

$$x=\frac{0±8\sqrt{17}}{2}$$

Now solve the equation x=\frac{0±8\sqrt{17}}{2} when ± is plus.

$$x=4\sqrt{17}$$

Now solve the equation x=\frac{0±8\sqrt{17}}{2} when ± is minus.

$$x=-4\sqrt{17}$$

The equation is now solved.

$$x=4\sqrt{17} x=-4\sqrt{17}$$