Solve 50^2=x^2+48^2

$${ 50 }^{ 2 } = { x }^{ 2 } + { 48 }^{ 2 }$$

Solve for x

$$x=14$$

$$x=-14$$

Steps Using Difference of Squares

Calculate 50 to the power of 2 and get 2500.

$$2500=x^{2}+48^{2}$$

Calculate 48 to the power of 2 and get 2304.

$$2500=x^{2}+2304$$

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

$$x^{2}+2304=2500$$

Subtract 2500 from both sides.

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

Subtract 2500 from 2304 to get -196.

$$x^{2}-196=0$$

Consider x^{2}-196. Rewrite x^{2}-196 as x^{2}-14^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-14\right)\left(x+14\right)=0$$

To find equation solutions, solve x-14=0 and x+14=0.

$$x=14 x=-14$$

Steps by Finding Square Root

Calculate 50 to the power of 2 and get 2500.

$$2500=x^{2}+48^{2}$$

Calculate 48 to the power of 2 and get 2304.

$$2500=x^{2}+2304$$

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

$$x^{2}+2304=2500$$

Subtract 2304 from both sides.

$$x^{2}=2500-2304$$

Subtract 2304 from 2500 to get 196.

$$x^{2}=196$$

Take the square root of both sides of the equation.

$$x=14 x=-14$$

Steps Using the Quadratic Formula

Calculate 50 to the power of 2 and get 2500.

$$2500=x^{2}+48^{2}$$

Calculate 48 to the power of 2 and get 2304.

$$2500=x^{2}+2304$$

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

$$x^{2}+2304=2500$$

Subtract 2500 from both sides.

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

Subtract 2500 from 2304 to get -196.

$$x^{2}-196=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -196 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-196\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-196\right)}}{2}$$

Multiply -4 times -196.

$$x=\frac{0±\sqrt{784}}{2}$$

Take the square root of 784.

$$x=\frac{0±28}{2}$$

Now solve the equation x=\frac{0±28}{2} when ± is plus. Divide 28 by 2.

$$x=14$$

Now solve the equation x=\frac{0±28}{2} when ± is minus. Divide -28 by 2.

$$x=-14$$

The equation is now solved.

$$x=14 x=-14$$