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

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

Solve for x

$$x=12\sqrt{2}\approx 16.970562748$$

$$x=-12\sqrt{2}\approx -16.970562748$$

Steps by Finding Square Root

Calculate 12 to the power of 2 and get 144.

$$144+12^{2}=x^{2}$$

Calculate 12 to the power of 2 and get 144.

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

Add 144 and 144 to get 288.

$$288=x^{2}$$

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

$$x^{2}=288$$

Take the square root of both sides of the equation.

$$x=12\sqrt{2} x=-12\sqrt{2}$$

Steps Using the Quadratic Formula

Calculate 12 to the power of 2 and get 144.

$$144+12^{2}=x^{2}$$

Calculate 12 to the power of 2 and get 144.

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

Add 144 and 144 to get 288.

$$288=x^{2}$$

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

$$x^{2}=288$$

Subtract 288 from both sides.

$$x^{2}-288=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -288 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-288\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-288\right)}}{2}$$

Multiply -4 times -288.

$$x=\frac{0±\sqrt{1152}}{2}$$

Take the square root of 1152.

$$x=\frac{0±24\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±24\sqrt{2}}{2} when ± is plus.

$$x=12\sqrt{2}$$

Now solve the equation x=\frac{0±24\sqrt{2}}{2} when ± is minus.

$$x=-12\sqrt{2}$$

The equation is now solved.

$$x=12\sqrt{2} x=-12\sqrt{2}$$