Solve 120^2=x^2+96^2

$${ 120 }^{ 2 } = { x }^{ 2 } + { 96 }^{ 2 }$$

Solve for x

$$x=72$$

$$x=-72$$

Steps Using Difference of Squares

Calculate 120 to the power of 2 and get 14400.

$$14400=x^{2}+96^{2}$$

Calculate 96 to the power of 2 and get 9216.

$$14400=x^{2}+9216$$

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

$$x^{2}+9216=14400$$

Subtract 14400 from both sides.

$$x^{2}[phone]=0$$

Subtract 14400 from 9216 to get -5184.

$$x^{2}-5184=0$$

Consider x^{2}-5184. Rewrite x^{2}-5184 as x^{2}-72^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-72\right)\left(x+72\right)=0$$

To find equation solutions, solve x-72=0 and x+72=0.

$$x=72 x=-72$$

Steps by Finding Square Root

Calculate 120 to the power of 2 and get 14400.

$$14400=x^{2}+96^{2}$$

Calculate 96 to the power of 2 and get 9216.

$$14400=x^{2}+9216$$

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

$$x^{2}+9216=14400$$

Subtract 9216 from both sides.

$$x^{2}=14400-9216$$

Subtract 9216 from 14400 to get 5184.

$$x^{2}=5184$$

Take the square root of both sides of the equation.

$$x=72 x=-72$$

Steps Using the Quadratic Formula

Calculate 120 to the power of 2 and get 14400.

$$14400=x^{2}+96^{2}$$

Calculate 96 to the power of 2 and get 9216.

$$14400=x^{2}+9216$$

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

$$x^{2}+9216=14400$$

Subtract 14400 from both sides.

$$x^{2}[phone]=0$$

Subtract 14400 from 9216 to get -5184.

$$x^{2}-5184=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -5184 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-5184\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-5184\right)}}{2}$$

Multiply -4 times -5184.

$$x=\frac{0±\sqrt{20736}}{2}$$

Take the square root of 20736.

$$x=\frac{0±144}{2}$$

Now solve the equation x=\frac{0±144}{2} when ± is plus. Divide 144 by 2.

$$x=72$$

Now solve the equation x=\frac{0±144}{2} when ± is minus. Divide -144 by 2.

$$x=-72$$

The equation is now solved.

$$x=72 x=-72$$