Algebra Examples

$3 x^{2} + X + 4 = 0$

Step 1

Subtract $4$ from both sides of the equation.

$3 x^{2} + X = - 4$

Step 2

Subtract $X$ from both sides of the equation.

$3 x^{2} = - 4 - X$

Step 3

Divide each term in $3 x^{2} = - 4 - X$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 x^{2} = - 4 - X$ by $3$ .

$\frac{3 x^{2}}{3} = \frac{- 4}{3} + \frac{- X}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 x^{2}}{3} = \frac{- 4}{3} + \frac{- X}{3}$

Step 3.2.1.2

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

$x^{2} = \frac{- 4}{3} + \frac{- X}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Move the negative in front of the fraction.

$x^{2} = - \frac{4}{3} + \frac{- X}{3}$

Step 3.3.1.2

Move the negative in front of the fraction.

$x^{2} = - \frac{4}{3} - \frac{X}{3}$

Step 4

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

$x = \pm \sqrt{- \frac{4}{3} - \frac{X}{3}}$

Step 5

Simplify $\pm \sqrt{- \frac{4}{3} - \frac{X}{3}}$ .

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Step 5.1

Factor $- 1$ out of $- \frac{4}{3} - \frac{X}{3}$ .

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Step 5.1.1

Reorder $- \frac{4}{3}$ and $- \frac{X}{3}$ .

$x = \pm \sqrt{- \frac{X}{3} - \frac{4}{3}}$

Step 5.1.2

Factor $- 1$ out of $- \frac{X}{3}$ .

$x = \pm \sqrt{- (\frac{X}{3}) - \frac{4}{3}}$

Step 5.1.3

Factor $- 1$ out of $- \frac{4}{3}$ .

$x = \pm \sqrt{- (\frac{X}{3}) - (\frac{4}{3})}$

Step 5.1.4

Factor $- 1$ out of $- (\frac{X}{3}) - (\frac{4}{3})$ .

$x = \pm \sqrt{- (\frac{X}{3} + \frac{4}{3})}$

Step 5.2

Combine the numerators over the common denominator.

$x = \pm \sqrt{- \frac{X + 4}{3}}$

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.

$x = \sqrt{- \frac{X + 4}{3}}$

Step 6.2

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

$x = - \sqrt{- \frac{X + 4}{3}}$

Step 6.3

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

$x = \sqrt{- \frac{X + 4}{3}}$

$x = - \sqrt{- \frac{X + 4}{3}}$

$x = \sqrt{- \frac{X + 4}{3}}$

$x = - \sqrt{- \frac{X + 4}{3}}$