Solve x^2=45^2+24^2

$${ x }^{ 2 } = { 45 }^{ 2 } + { 24 }^{ 2 }$$

Solve for x

$$x=-51$$

$$x=51$$

Steps Using Difference of Squares

Calculate 45 to the power of 2 and get 2025.

$$x^{2}=2025+24^{2}$$

Calculate 24 to the power of 2 and get 576.

$$x^{2}=2025+576$$

Add 2025 and 576 to get 2601.

$$x^{2}=2601$$

Subtract 2601 from both sides.

$$x^{2}-2601=0$$

Consider x^{2}-2601. Rewrite x^{2}-2601 as x^{2}-51^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-51\right)\left(x+51\right)=0$$

To find equation solutions, solve x-51=0 and x+51=0.

$$x=51 x=-51$$

Steps by Finding Square Root

Calculate 45 to the power of 2 and get 2025.

$$x^{2}=2025+24^{2}$$

Calculate 24 to the power of 2 and get 576.

$$x^{2}=2025+576$$

Add 2025 and 576 to get 2601.

$$x^{2}=2601$$

Take the square root of both sides of the equation.

$$x=51 x=-51$$

Steps Using the Quadratic Formula

Calculate 45 to the power of 2 and get 2025.

$$x^{2}=2025+24^{2}$$

Calculate 24 to the power of 2 and get 576.

$$x^{2}=2025+576$$

Add 2025 and 576 to get 2601.

$$x^{2}=2601$$

Subtract 2601 from both sides.

$$x^{2}-2601=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -2601 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2601\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2601\right)}}{2}$$

Multiply -4 times -2601.

$$x=\frac{0±\sqrt{10404}}{2}$$

Take the square root of 10404.

$$x=\frac{0±102}{2}$$

Now solve the equation x=\frac{0±102}{2} when ± is plus. Divide 102 by 2.

$$x=51$$

Now solve the equation x=\frac{0±102}{2} when ± is minus. Divide -102 by 2.

$$x=-51$$

The equation is now solved.

$$x=51 x=-51$$