Solve x^2+{left(16sqrt{2}right)}^2={left(17sqrt{2}right)}^2

$${ x }^{ 2 } + { \left(16 \sqrt{ 2 } \right) }^{ 2 } = { \left(17 \sqrt{ 2 } \right) }^{ 2 }$$

Solve for x

$$x=\sqrt{66}\approx 8.124038405$$

$$x=-\sqrt{66}\approx -8.124038405$$

Steps by Finding Square Root

Expand \left(16\sqrt{2}\right)^{2}.

$$x^{2}+16^{2}\left(\sqrt{2}\right)^{2}=\left(17\sqrt{2}\right)^{2}$$

Calculate 16 to the power of 2 and get 256.

$$x^{2}+256\left(\sqrt{2}\right)^{2}=\left(17\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$x^{2}+256\times 2=\left(17\sqrt{2}\right)^{2}$$

Multiply 256 and 2 to get 512.

$$x^{2}+512=\left(17\sqrt{2}\right)^{2}$$

Expand \left(17\sqrt{2}\right)^{2}.

$$x^{2}+512=17^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 17 to the power of 2 and get 289.

$$x^{2}+512=289\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$x^{2}+512=289\times 2$$

Multiply 289 and 2 to get 578.

$$x^{2}+512=578$$

Subtract 512 from both sides.

$$x^{2}=578-512$$

Subtract 512 from 578 to get 66.

$$x^{2}=66$$

Take the square root of both sides of the equation.

$$x=\sqrt{66} x=-\sqrt{66}$$

Steps Using the Quadratic Formula

Expand \left(16\sqrt{2}\right)^{2}.

$$x^{2}+16^{2}\left(\sqrt{2}\right)^{2}=\left(17\sqrt{2}\right)^{2}$$

Calculate 16 to the power of 2 and get 256.

$$x^{2}+256\left(\sqrt{2}\right)^{2}=\left(17\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$x^{2}+256\times 2=\left(17\sqrt{2}\right)^{2}$$

Multiply 256 and 2 to get 512.

$$x^{2}+512=\left(17\sqrt{2}\right)^{2}$$

Expand \left(17\sqrt{2}\right)^{2}.

$$x^{2}+512=17^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 17 to the power of 2 and get 289.

$$x^{2}+512=289\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$x^{2}+512=289\times 2$$

Multiply 289 and 2 to get 578.

$$x^{2}+512=578$$

Subtract 578 from both sides.

$$x^{2}+512-578=0$$

Subtract 578 from 512 to get -66.

$$x^{2}-66=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -66 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-66\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-66\right)}}{2}$$

Multiply -4 times -66.

$$x=\frac{0±\sqrt{264}}{2}$$

Take the square root of 264.

$$x=\frac{0±2\sqrt{66}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{66}}{2} when ± is plus.

$$x=\sqrt{66}$$

Now solve the equation x=\frac{0±2\sqrt{66}}{2} when ± is minus.

$$x=-\sqrt{66}$$

The equation is now solved.

$$x=\sqrt{66} x=-\sqrt{66}$$