Solve for x 25(x^2-5)+14=10

$25 (x^{2} - 5) + 14 = 10$

Step 1

Simplify $25 (x^{2} - 5) + 14$ .

Simplify each term.

Apply the distributive property.

$25 x^{2} + 25 \cdot - 5 + 14 = 10$

Multiply $25$ by $- 5$ .

$25 x^{2} - 125 + 14 = 10$

Add $- 125$ and $14$ .

$25 x^{2} - 111 = 10$

Step 2

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

Add $111$ to both sides of the equation.

$25 x^{2} = 10 + 111$

Add $10$ and $111$ .

$25 x^{2} = 121$

Step 3

Divide each term in $25 x^{2} = 121$ by $25$ and simplify.

Divide each term in $25 x^{2} = 121$ by $25$ .

$\frac{25 x^{2}}{25} = \frac{121}{25}$

Simplify the left side.

Cancel the common factor of $25$ .

Cancel the common factor.

$\frac{25 x^{2}}{25} = \frac{121}{25}$

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

$x^{2} = \frac{121}{25}$

Step 4

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

$x = \pm \sqrt{\frac{121}{25}}$

Step 5

Simplify $\pm \sqrt{\frac{121}{25}}$ .

Rewrite $\sqrt{\frac{121}{25}}$ as $\frac{\sqrt{121}}{\sqrt{25}}$ .

$x = \pm \frac{\sqrt{121}}{\sqrt{25}}$

Simplify the numerator.

Rewrite $121$ as $11^{2}$ .

$x = \pm \frac{\sqrt{11^{2}}}{\sqrt{25}}$

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

$x = \pm \frac{11}{\sqrt{25}}$

Simplify the denominator.

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

$x = \pm \frac{11}{\sqrt{5^{2}}}$

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

$x = \pm \frac{11}{5}$

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.

$x = \frac{11}{5}$

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

$x = - \frac{11}{5}$

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

$x = \frac{11}{5}, - \frac{11}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11}{5}, - \frac{11}{5}$

Decimal Form:

$x = 2.2, - 2.2$

Mixed Number Form:

$x = 2 \frac{1}{5}, - 2 \frac{1}{5}$

Solve for x 25(x^2-5)+14=10

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