Linear Algebra Examples

$y = \frac{1}{8} x^{2}$

Step 1

Rewrite the equation as $\frac{1}{8} x^{2} = y$ .

$\frac{1}{8} x^{2} = y$

Step 2

Multiply both sides of the equation by $8$ .

$8 (\frac{1}{8} x^{2}) = 8 y$

Step 3

Simplify the left side.

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Step 3.1

Simplify $8 (\frac{1}{8} x^{2})$ .

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Step 3.1.1

Combine $\frac{1}{8}$ and $x^{2}$ .

$8 \frac{x^{2}}{8} = 8 y$

Step 3.1.2

Cancel the common factor of $8$ .

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Step 3.1.2.1

Cancel the common factor.

$8 \frac{x^{2}}{8} = 8 y$

Step 3.1.2.2

Rewrite the expression.

$x^{2} = 8 y$

Step 4

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

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

Step 5

Simplify $\pm \sqrt{8 y}$ .

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Step 5.1

Rewrite $8 y$ as $2^{2} \cdot (2 y)$ .

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Step 5.1.1

Factor $4$ out of $8$ .

$x = \pm \sqrt{4 (2) y}$

Step 5.1.2

Rewrite $4$ as $2^{2}$ .

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

Step 5.1.3

Add parentheses.

$x = \pm \sqrt{2^{2} \cdot (2 y)}$

Step 5.2

Pull terms out from under the radical.

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

Step 6

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

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Step 6.1

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

$x = 2 \sqrt{2 y}$

Step 6.2

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

$x = - 2 \sqrt{2 y}$

Step 6.3

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

$x = 2 \sqrt{2 y}$

$x = - 2 \sqrt{2 y}$

$x = 2 \sqrt{2 y}$

$x = - 2 \sqrt{2 y}$