Solve 5^2*10^2=x^2

$${ 5 }^{ 2 } \times { 10 }^{ 2 } = { x }^{ 2 }$$

Solve for x

$$x=50$$

$$x=-50$$

Steps Using Difference of Squares

Calculate 5 to the power of 2 and get 25.

$$25\times 10^{2}=x^{2}$$

Calculate 10 to the power of 2 and get 100.

$$25\times 100=x^{2}$$

Multiply 25 and 100 to get 2500.

$$2500=x^{2}$$

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

$$x^{2}=2500$$

Subtract 2500 from both sides.

$$x^{2}-2500=0$$

Consider x^{2}-2500. Rewrite x^{2}-2500 as x^{2}-50^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-50\right)\left(x+50\right)=0$$

To find equation solutions, solve x-50=0 and x+50=0.

$$x=50 x=-50$$

Steps by Finding Square Root

Calculate 5 to the power of 2 and get 25.

$$25\times 10^{2}=x^{2}$$

Calculate 10 to the power of 2 and get 100.

$$25\times 100=x^{2}$$

Multiply 25 and 100 to get 2500.

$$2500=x^{2}$$

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

$$x^{2}=2500$$

Take the square root of both sides of the equation.

$$x=50 x=-50$$

Steps Using the Quadratic Formula

Calculate 5 to the power of 2 and get 25.

$$25\times 10^{2}=x^{2}$$

Calculate 10 to the power of 2 and get 100.

$$25\times 100=x^{2}$$

Multiply 25 and 100 to get 2500.

$$2500=x^{2}$$

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

$$x^{2}=2500$$

Subtract 2500 from both sides.

$$x^{2}-2500=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -2500 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2500\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2500\right)}}{2}$$

Multiply -4 times -2500.

$$x=\frac{0±\sqrt{10000}}{2}$$

Take the square root of 10000.

$$x=\frac{0±100}{2}$$

Now solve the equation x=\frac{0±100}{2} when ± is plus. Divide 100 by 2.

$$x=50$$

Now solve the equation x=\frac{0±100}{2} when ± is minus. Divide -100 by 2.

$$x=-50$$

The equation is now solved.

$$x=50 x=-50$$