Solve 5^14x^2-5^12=0

$$5 ^ { 14 } x ^ { 2 } - 5 ^ { 12 } = 0$$

Solve for x

$$x=\frac{1}{5}=0.2$$

$$x=-\frac{1}{5}=-0.2$$

Steps Using Difference of Squares

Calculate 5 to the power of 14 and get 6103515625.

$$6103515625x^{2}-5^{12}=0$$

Calculate 5 to the power of 12 and get 244140625.

$$6103515625x^{2}-244140625=0$$

Divide both sides by 244140625.

$$25x^{2}-1=0$$

Consider 25x^{2}-1. Rewrite 25x^{2}-1 as \left(5x\right)^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(5x-1\right)\left(5x+1\right)=0$$

To find equation solutions, solve 5x-1=0 and 5x+1=0.

$$x=\frac{1}{5} x=-\frac{1}{5}$$

Steps by Finding Square Root

Calculate 5 to the power of 14 and get 6103515625.

$$6103515625x^{2}-5^{12}=0$$

Calculate 5 to the power of 12 and get 244140625.

$$6103515625x^{2}-244140625=0$$

Add 244140625 to both sides. Anything plus zero gives itself.

$$6103515625x^{2}=244140625$$

Divide both sides by 6103515625.

$$x^{2}=\frac{244140625}{6103515625}$$

Reduce the fraction \frac{244140625}{6103515625} to lowest terms by extracting and canceling out 244140625.

$$x^{2}=\frac{1}{25}$$

Take the square root of both sides of the equation.

$$x=\frac{1}{5} x=-\frac{1}{5}$$

Steps Using the Quadratic Formula

Calculate 5 to the power of 14 and get 6103515625.

$$6103515625x^{2}-5^{12}=0$$

Calculate 5 to the power of 12 and get 244140625.

$$6103515625x^{2}-244140625=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6103515625 for a, 0 for b, and -244140625 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6103515625\left(-244140625\right)}}{2\times 6103515625}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6103515625\left(-244140625\right)}}{2\times 6103515625}$$

Multiply -4 times 6103515625.

$$x=\frac{0±\sqrt{-24414062500\left(-244140625\right)}}{2\times 6103515625}$$

Multiply -24414062500 times -244140625.

$$x=\frac{0±\sqrt{5960464477539062500}}{2\times 6103515625}$$

Take the square root of 5960464477539062500.

$$x=\frac{0±2441406250}{2\times 6103515625}$$

Multiply 2 times 6103515625.

$$x=\frac{0±2441406250}{12207031250}$$

Now solve the equation x=\frac{0±2441406250}{12207031250} when ± is plus. Reduce the fraction \frac{2441406250}{12207031250} to lowest terms by extracting and canceling out 2441406250.

$$x=\frac{1}{5}$$

Now solve the equation x=\frac{0±2441406250}{12207031250} when ± is minus. Reduce the fraction \frac{-2441406250}{12207031250} to lowest terms by extracting and canceling out 2441406250.

$$x=-\frac{1}{5}$$

The equation is now solved.

$$x=\frac{1}{5} x=-\frac{1}{5}$$