Solve x^2=64^2+24^2

$${ x }^{ 2 } = { 64 }^{ 2 } + { 24 }^{ 2 }$$

Solve for x

$$x=8\sqrt{73}\approx 68.352029963$$

$$x=-8\sqrt{73}\approx -68.352029963$$

Steps by Finding Square Root

Calculate 64 to the power of 2 and get 4096.

$$x^{2}=4096+24^{2}$$

Calculate 24 to the power of 2 and get 576.

$$x^{2}=4096+576$$

Add 4096 and 576 to get 4672.

$$x^{2}=4672$$

Take the square root of both sides of the equation.

$$x=8\sqrt{73} x=-8\sqrt{73}$$

Steps Using the Quadratic Formula

Calculate 64 to the power of 2 and get 4096.

$$x^{2}=4096+24^{2}$$

Calculate 24 to the power of 2 and get 576.

$$x^{2}=4096+576$$

Add 4096 and 576 to get 4672.

$$x^{2}=4672$$

Subtract 4672 from both sides.

$$x^{2}-4672=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -4672 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-4672\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-4672\right)}}{2}$$

Multiply -4 times -4672.

$$x=\frac{0±\sqrt{18688}}{2}$$

Take the square root of 18688.

$$x=\frac{0±16\sqrt{73}}{2}$$

Now solve the equation x=\frac{0±16\sqrt{73}}{2} when ± is plus.

$$x=8\sqrt{73}$$

Now solve the equation x=\frac{0±16\sqrt{73}}{2} when ± is minus.

$$x=-8\sqrt{73}$$

The equation is now solved.

$$x=8\sqrt{73} x=-8\sqrt{73}$$