Solve x^2=6^2+33^2

$${ x }^{ 2 } = { 6 }^{ 2 } + { 33 }^{ 2 }$$

Solve for x

$$x=15\sqrt{5}\approx 33.541019662$$

$$x=-15\sqrt{5}\approx -33.541019662$$

Steps by Finding Square Root

Calculate 6 to the power of 2 and get 36.

$$x^{2}=36+33^{2}$$

Calculate 33 to the power of 2 and get 1089.

$$x^{2}=36+1089$$

Add 36 and 1089 to get 1125.

$$x^{2}=1125$$

Take the square root of both sides of the equation.

$$x=15\sqrt{5} x=-15\sqrt{5}$$

Steps Using the Quadratic Formula

Calculate 6 to the power of 2 and get 36.

$$x^{2}=36+33^{2}$$

Calculate 33 to the power of 2 and get 1089.

$$x^{2}=36+1089$$

Add 36 and 1089 to get 1125.

$$x^{2}=1125$$

Subtract 1125 from both sides.

$$x^{2}-1125=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1125 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1125\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1125\right)}}{2}$$

Multiply -4 times -1125.

$$x=\frac{0±\sqrt{4500}}{2}$$

Take the square root of 4500.

$$x=\frac{0±30\sqrt{5}}{2}$$

Now solve the equation x=\frac{0±30\sqrt{5}}{2} when ± is plus.

$$x=15\sqrt{5}$$

Now solve the equation x=\frac{0±30\sqrt{5}}{2} when ± is minus.

$$x=-15\sqrt{5}$$

The equation is now solved.

$$x=15\sqrt{5} x=-15\sqrt{5}$$