Solve 16^2+8^2=x^2

$$16 ^ { 2 } + 8 ^ { 2 } = x ^ { 2 }$$

Solve for x

$$x=8\sqrt{5}\approx 17.88854382$$

$$x=-8\sqrt{5}\approx -17.88854382$$

Steps by Finding Square Root

Calculate 16 to the power of 2 and get 256.

$$256+8^{2}=x^{2}$$

Calculate 8 to the power of 2 and get 64.

$$256+64=x^{2}$$

Add 256 and 64 to get 320.

$$320=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=320$$

Take the square root of both sides of the equation.

$$x=8\sqrt{5} x=-8\sqrt{5}$$

Steps Using the Quadratic Formula

Calculate 16 to the power of 2 and get 256.

$$256+8^{2}=x^{2}$$

Calculate 8 to the power of 2 and get 64.

$$256+64=x^{2}$$

Add 256 and 64 to get 320.

$$320=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=320$$

Subtract 320 from both sides.

$$x^{2}-320=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -320 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-320\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-320\right)}}{2}$$

Multiply -4 times -320.

$$x=\frac{0±\sqrt{1280}}{2}$$

Take the square root of 1280.

$$x=\frac{0±16\sqrt{5}}{2}$$

Now solve the equation x=\frac{0±16\sqrt{5}}{2} when ± is plus.

$$x=8\sqrt{5}$$

Now solve the equation x=\frac{0±16\sqrt{5}}{2} when ± is minus.

$$x=-8\sqrt{5}$$

The equation is now solved.

$$x=8\sqrt{5} x=-8\sqrt{5}$$