Solve 8^2+12^2=x^2

$${ 8 }^{ 2 } + { 12 }^{ 2 } = { x }^{ 2 }$$

Solve for x

$$x=4\sqrt{13}\approx 14.422205102$$

$$x=-4\sqrt{13}\approx -14.422205102$$

Steps by Finding Square Root

Calculate 8 to the power of 2 and get 64.

$$64+12^{2}=x^{2}$$

Calculate 12 to the power of 2 and get 144.

$$64+144=x^{2}$$

Add 64 and 144 to get 208.

$$208=x^{2}$$

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

$$x^{2}=208$$

Take the square root of both sides of the equation.

$$x=4\sqrt{13} x=-4\sqrt{13}$$

Steps Using the Quadratic Formula

Calculate 8 to the power of 2 and get 64.

$$64+12^{2}=x^{2}$$

Calculate 12 to the power of 2 and get 144.

$$64+144=x^{2}$$

Add 64 and 144 to get 208.

$$208=x^{2}$$

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

$$x^{2}=208$$

Subtract 208 from both sides.

$$x^{2}-208=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -208 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-208\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-208\right)}}{2}$$

Multiply -4 times -208.

$$x=\frac{0±\sqrt{832}}{2}$$

Take the square root of 832.

$$x=\frac{0±8\sqrt{13}}{2}$$

Now solve the equation x=\frac{0±8\sqrt{13}}{2} when ± is plus.

$$x=4\sqrt{13}$$

Now solve the equation x=\frac{0±8\sqrt{13}}{2} when ± is minus.

$$x=-4\sqrt{13}$$

The equation is now solved.

$$x=4\sqrt{13} x=-4\sqrt{13}$$