Solve 25^2=x^2+24^2

$${ 25 }^{ 2 } = { x }^{ 2 } + { 24 }^{ 2 }$$

Solve for x

$$x=7$$

$$x=-7$$

Steps Using Difference of Squares

Calculate 25 to the power of 2 and get 625.

$$625=x^{2}+24^{2}$$

Calculate 24 to the power of 2 and get 576.

$$625=x^{2}+576$$

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

$$x^{2}+576=625$$

Subtract 625 from both sides.

$$x^{2}+576-625=0$$

Subtract 625 from 576 to get -49.

$$x^{2}-49=0$$

Consider x^{2}-49. Rewrite x^{2}-49 as x^{2}-7^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-7\right)\left(x+7\right)=0$$

To find equation solutions, solve x-7=0 and x+7=0.

$$x=7 x=-7$$

Steps by Finding Square Root

Calculate 25 to the power of 2 and get 625.

$$625=x^{2}+24^{2}$$

Calculate 24 to the power of 2 and get 576.

$$625=x^{2}+576$$

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

$$x^{2}+576=625$$

Subtract 576 from both sides.

$$x^{2}=625-576$$

Subtract 576 from 625 to get 49.

$$x^{2}=49$$

Take the square root of both sides of the equation.

$$x=7 x=-7$$

Steps Using the Quadratic Formula

Calculate 25 to the power of 2 and get 625.

$$625=x^{2}+24^{2}$$

Calculate 24 to the power of 2 and get 576.

$$625=x^{2}+576$$

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

$$x^{2}+576=625$$

Subtract 625 from both sides.

$$x^{2}+576-625=0$$

Subtract 625 from 576 to get -49.

$$x^{2}-49=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -49 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-49\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-49\right)}}{2}$$

Multiply -4 times -49.

$$x=\frac{0±\sqrt{196}}{2}$$

Take the square root of 196.

$$x=\frac{0±14}{2}$$

Now solve the equation x=\frac{0±14}{2} when ± is plus. Divide 14 by 2.

$$x=7$$

Now solve the equation x=\frac{0±14}{2} when ± is minus. Divide -14 by 2.

$$x=-7$$

The equation is now solved.

$$x=7 x=-7$$