Solve for x 1/4x^2-7=25

$\frac{1}{4} x^{2} - 7 = 25$

Step 1

Combine $\frac{1}{4}$ and $x^{2}$ .

$\frac{x^{2}}{4} - 7 = 25$

Step 2

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

Add $7$ to both sides of the equation.

$\frac{x^{2}}{4} = 25 + 7$

Add $25$ and $7$ .

$\frac{x^{2}}{4} = 32$

Step 3

Multiply both sides of the equation by $4$ .

$4 \frac{x^{2}}{4} = 4 \cdot 32$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$4 \frac{x^{2}}{4} = 4 \cdot 32$

Rewrite the expression.

$x^{2} = 4 \cdot 32$

Simplify the right side.

Multiply $4$ by $32$ .

$x^{2} = 128$

Step 5

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

$x = \pm \sqrt{128}$

Step 6

Simplify $\pm \sqrt{128}$ .

Rewrite $128$ as $8^{2} \cdot 2$ .

Factor $64$ out of $128$ .

$x = \pm \sqrt{64 (2)}$

Rewrite $64$ as $8^{2}$ .

$x = \pm \sqrt{8^{2} \cdot 2}$

Pull terms out from under the radical.

$x = \pm 8 \sqrt{2}$

Step 7

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.

$x = 8 \sqrt{2}$

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

$x = - 8 \sqrt{2}$

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

$x = 8 \sqrt{2}, - 8 \sqrt{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = 8 \sqrt{2}, - 8 \sqrt{2}$

Decimal Form:

$x = 11.31370849 \dots, - 11.31370849 \dots$

Solve for x 1/4x^2-7=25

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