Solve x^2=8^2+8^2

$${ x }^{ 2 } = { 8 }^{ 2 } + { 8 }^{ 2 }$$

Solve for x

$$x=8\sqrt{2}\approx 11.313708499$$

$$x=-8\sqrt{2}\approx -11.313708499$$

Steps by Finding Square Root

Calculate 8 to the power of 2 and get 64.

$$x^{2}=64+8^{2}$$

Calculate 8 to the power of 2 and get 64.

$$x^{2}=64+64$$

Add 64 and 64 to get 128.

$$x^{2}=128$$

Take the square root of both sides of the equation.

$$x=8\sqrt{2} x=-8\sqrt{2}$$

Steps Using the Quadratic Formula

Calculate 8 to the power of 2 and get 64.

$$x^{2}=64+8^{2}$$

Calculate 8 to the power of 2 and get 64.

$$x^{2}=64+64$$

Add 64 and 64 to get 128.

$$x^{2}=128$$

Subtract 128 from both sides.

$$x^{2}-128=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -128 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-128\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-128\right)}}{2}$$

Multiply -4 times -128.

$$x=\frac{0±\sqrt{512}}{2}$$

Take the square root of 512.

$$x=\frac{0±16\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±16\sqrt{2}}{2} when ± is plus.

$$x=8\sqrt{2}$$

Now solve the equation x=\frac{0±16\sqrt{2}}{2} when ± is minus.

$$x=-8\sqrt{2}$$

The equation is now solved.

$$x=8\sqrt{2} x=-8\sqrt{2}$$