Solve 65^2=x^2-56^2

$$65 ^ { 2 } = x ^ { 2 } - 56 ^ { 2 }$$

Solve for x

$$x=\sqrt{7361}\approx 85.796270315$$

$$x=-\sqrt{7361}\approx -85.796270315$$

Steps by Finding Square Root

Calculate 65 to the power of 2 and get 4225.

$$4225=x^{2}-56^{2}$$

Calculate 56 to the power of 2 and get 3136.

$$4225=x^{2}-3136$$

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

$$x^{2}-3136=4225$$

Add 3136 to both sides.

$$x^{2}=4225+3136$$

Add 4225 and 3136 to get 7361.

$$x^{2}=7361$$

Take the square root of both sides of the equation.

$$x=\sqrt{7361} x=-\sqrt{7361}$$

Steps Using the Quadratic Formula

Calculate 65 to the power of 2 and get 4225.

$$4225=x^{2}-56^{2}$$

Calculate 56 to the power of 2 and get 3136.

$$4225=x^{2}-3136$$

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

$$x^{2}-3136=4225$$

Subtract 4225 from both sides.

$$x^{2}-3136-4225=0$$

Subtract 4225 from -3136 to get -7361.

$$x^{2}-7361=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -7361 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-7361\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-7361\right)}}{2}$$

Multiply -4 times -7361.

$$x=\frac{0±\sqrt{29444}}{2}$$

Take the square root of 29444.

$$x=\frac{0±2\sqrt{7361}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{7361}}{2} when ± is plus.

$$x=\sqrt{7361}$$

Now solve the equation x=\frac{0±2\sqrt{7361}}{2} when ± is minus.

$$x=-\sqrt{7361}$$

The equation is now solved.

$$x=\sqrt{7361} x=-\sqrt{7361}$$