Solve for x 25(x^2+1)-12=14

$25 (x^{2} + 1) - 12 = 14$

Step 1

Simplify $25 (x^{2} + 1) - 12$ .

Simplify each term.

Apply the distributive property.

$25 x^{2} + 25 \cdot 1 - 12 = 14$

Multiply $25$ by $1$ .

$25 x^{2} + 25 - 12 = 14$

Subtract $12$ from $25$ .

$25 x^{2} + 13 = 14$

Step 2

Move all terms not containing $x$ to the right side of the equation.

Subtract $13$ from both sides of the equation.

$25 x^{2} = 14 - 13$

Subtract $13$ from $14$ .

$25 x^{2} = 1$

Step 3

Divide each term in $25 x^{2} = 1$ by $25$ and simplify.

Divide each term in $25 x^{2} = 1$ by $25$ .

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

Simplify the left side.

Cancel the common factor of $25$ .

Cancel the common factor.

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

Divide $x^{2}$ by $1$ .

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

Step 4

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{\frac{1}{25}}$

Step 5

Simplify $\pm \sqrt{\frac{1}{25}}$ .

Rewrite $\sqrt{\frac{1}{25}}$ as $\frac{\sqrt{1}}{\sqrt{25}}$ .

$x = \pm \frac{\sqrt{1}}{\sqrt{25}}$

Any root of $1$ is $1$ .

$x = \pm \frac{1}{\sqrt{25}}$

Simplify the denominator.

Rewrite $25$ as $5^{2}$ .

$x = \pm \frac{1}{\sqrt{5^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

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

Step 6

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

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

Next, use the negative value of the $\pm$ to find the second solution.

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

The complete solution is the result of both the positive and negative portions of the solution.

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.2, - 0.2$

Solve for x 25(x^2+1)-12=14

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