Algebra Examples

$x = - 8 y^{2}$

Step 1

Solve the equation for $y$ .

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Step 1.1

Rewrite the equation as $- 8 y^{2} = x$ .

$- 8 y^{2} = x$

Step 1.2

Divide each term in $- 8 y^{2} = x$ by $- 8$ and simplify.

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Step 1.2.1

Divide each term in $- 8 y^{2} = x$ by $- 8$ .

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

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 8$ .

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Step 1.2.2.1.1

Cancel the common factor.

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

Step 1.2.2.1.2

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

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

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Move the negative in front of the fraction.

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

Step 1.3

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

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

Step 1.4

Simplify $\pm \sqrt{- \frac{x}{8}}$ .

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Step 1.4.1

Rewrite $- \frac{x}{8}$ as ${(\frac{1^{2}}{2})}^{2} \cdot (- \frac{x}{2})$ .

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Step 1.4.1.1

Factor the perfect power $1^{2}$ out of $x$ .

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

Step 1.4.1.2

Factor the perfect power $2^{2}$ out of $8$ .

$y = \pm \sqrt{- \frac{1^{2} x}{2^{2} \cdot 2}}$

Step 1.4.1.3

Rearrange the fraction $\frac{1^{2} x}{2^{2} \cdot 2}$ .

$y = \pm \sqrt{- ({(\frac{1}{2})}^{2} \frac{x}{2})}$

Step 1.4.1.4

Reorder $- 1$ and ${(\frac{1}{2})}^{2}$ .

$y = \pm \sqrt{{(\frac{1}{2})}^{2} \cdot - 1 \frac{x}{2}}$

Step 1.4.1.5

Rewrite $1$ as $1^{2}$ .

$y = \pm \sqrt{{(\frac{1^{2}}{2})}^{2} \cdot - 1 \frac{x}{2}}$

Step 1.4.1.6

Add parentheses.

$y = \pm \sqrt{{(\frac{1^{2}}{2})}^{2} \cdot (- \frac{x}{2})}$

Step 1.4.2

Pull terms out from under the radical.

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

Step 1.4.3

One to any power is one.

$y = \pm \frac{1}{2} \sqrt{- \frac{x}{2}}$

Step 1.4.4

Combine $\frac{1}{2}$ and $\sqrt{- \frac{x}{2}}$ .

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

Step 1.5

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

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Step 1.5.1

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

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

Step 1.5.2

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

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

Step 1.5.3

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

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

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

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

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

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

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

Step 2

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be $0$ or $1$ for each of its variables. In this case, the degree of the variable in the equation violates the linear equation definition, which means that the equation is not a linear equation.

Not Linear