Solve x^2=144+128-2*8sqrt{2}*12*0.7

$${ x }^{ 2 } =144+128-2 \times 8 \sqrt{ 2 } \times 12 \times 0.7$$

Solve for x (complex solution)

$$x=-\sqrt{-\frac{672\sqrt{2}}{5}+272}\approx -9.051502484$$

$$x=\sqrt{-\frac{672\sqrt{2}}{5}+272}\approx 9.051502484$$

Steps by Finding Square Root

Add 144 and 128 to get 272.

$$x^{2}=272-0.7\times 2\times 8\times 12\sqrt{2}$$

Multiply 0.7 and 2 to get 1.4.

$$x^{2}=272-1.4\times 8\times 12\sqrt{2}$$

Multiply 1.4 and 8 to get 11.2.

$$x^{2}=272-11.2\times 12\sqrt{2}$$

Multiply 11.2 and 12 to get 134.4.

$$x^{2}=272-134.4\sqrt{2}$$

The equation is now solved.

$$x=\frac{4\sqrt{425-210\sqrt{2}}}{5} x=-\frac{4\sqrt{425-210\sqrt{2}}}{5}$$

Steps Using the Quadratic Formula

Add 144 and 128 to get 272.

$$x^{2}=272-0.7\times 2\times 8\times 12\sqrt{2}$$

Multiply 0.7 and 2 to get 1.4.

$$x^{2}=272-1.4\times 8\times 12\sqrt{2}$$

Multiply 1.4 and 8 to get 11.2.

$$x^{2}=272-11.2\times 12\sqrt{2}$$

Multiply 11.2 and 12 to get 134.4.

$$x^{2}=272-134.4\sqrt{2}$$

Subtract 272 from both sides.

$$x^{2}-272=-134.4\sqrt{2}$$

Add 134.4\sqrt{2} to both sides.

$$x^{2}-272+134.4\sqrt{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$x^{2}+\frac{672\sqrt{2}}{5}-272=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -272+\frac{672\sqrt{2}}{5} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(\frac{672\sqrt{2}}{5}-272\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(\frac{672\sqrt{2}}{5}-272\right)}}{2}$$

Multiply -4 times -272+\frac{672\sqrt{2}}{5}.

$$x=\frac{0±\sqrt{-\frac{2688\sqrt{2}}{5}+1088}}{2}$$

Take the square root of 1088-\frac{2688\sqrt{2}}{5}.

$$x=\frac{0±\frac{8\sqrt{425-210\sqrt{2}}}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{8\sqrt{425-210\sqrt{2}}}{5}}{2} when ± is plus.

$$x=\frac{4\sqrt{425-210\sqrt{2}}}{5}$$

Now solve the equation x=\frac{0±\frac{8\sqrt{425-210\sqrt{2}}}{5}}{2} when ± is minus.

$$x=-\frac{4\sqrt{425-210\sqrt{2}}}{5}$$

The equation is now solved.

$$x=\frac{4\sqrt{425-210\sqrt{2}}}{5} x=-\frac{4\sqrt{425-210\sqrt{2}}}{5}$$

Solve for x

$$x = \frac{4 \sqrt{425 - 210 \sqrt{2}}}{5} \approx 9.051502484$$

$$x = -\frac{4 \sqrt{425 - 210 \sqrt{2}}}{5} \approx -9.051502484$$