Solve 60^2+80^2=x^2

$${ 60 }^{ 2 } + { 80 }^{ 2 } = { x }^{ 2 }$$

Solve for x

$$x=100$$

$$x=-100$$

Steps Using Difference of Squares

Calculate 60 to the power of 2 and get 3600.

$$3600+80^{2}=x^{2}$$

Calculate 80 to the power of 2 and get 6400.

$$3600+6400=x^{2}$$

Add 3600 and 6400 to get 10000.

$$10000=x^{2}$$

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

$$x^{2}=10000$$

Subtract 10000 from both sides.

$$x^{2}-10000=0$$

Consider x^{2}-10000. Rewrite x^{2}-10000 as x^{2}-100^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-100\right)\left(x+100\right)=0$$

To find equation solutions, solve x-100=0 and x+100=0.

$$x=100 x=-100$$

Steps by Finding Square Root

Calculate 60 to the power of 2 and get 3600.

$$3600+80^{2}=x^{2}$$

Calculate 80 to the power of 2 and get 6400.

$$3600+6400=x^{2}$$

Add 3600 and 6400 to get 10000.

$$10000=x^{2}$$

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

$$x^{2}=10000$$

Take the square root of both sides of the equation.

$$x=100 x=-100$$

Steps Using the Quadratic Formula

Calculate 60 to the power of 2 and get 3600.

$$3600+80^{2}=x^{2}$$

Calculate 80 to the power of 2 and get 6400.

$$3600+6400=x^{2}$$

Add 3600 and 6400 to get 10000.

$$10000=x^{2}$$

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

$$x^{2}=10000$$

Subtract 10000 from both sides.

$$x^{2}-10000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -10000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-10000\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-10000\right)}}{2}$$

Multiply -4 times -10000.

$$x=\frac{0±\sqrt{40000}}{2}$$

Take the square root of 40000.

$$x=\frac{0±200}{2}$$

Now solve the equation x=\frac{0±200}{2} when ± is plus. Divide 200 by 2.

$$x=100$$

Now solve the equation x=\frac{0±200}{2} when ± is minus. Divide -200 by 2.

$$x=-100$$

The equation is now solved.

$$x=100 x=-100$$