Algebra Examples

$- 2 x^{2} + 5 x + 6 = 4 x^{2} + 5 x$

Step 1

Move all terms containing $x$ to the left side of the equation.

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Step 1.1

Subtract $4 x^{2}$ from both sides of the equation.

$- 2 x^{2} + 5 x + 6 - 4 x^{2} = 5 x$

Step 1.2

Subtract $5 x$ from both sides of the equation.

$- 2 x^{2} + 5 x + 6 - 4 x^{2} - 5 x = 0$

Step 1.3

Combine the opposite terms in $- 2 x^{2} + 5 x + 6 - 4 x^{2} - 5 x$ .

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Step 1.3.1

Subtract $5 x$ from $5 x$ .

$- 2 x^{2} + 6 - 4 x^{2} + 0 = 0$

Step 1.3.2

Add $- 2 x^{2} + 6 - 4 x^{2}$ and $0$ .

$- 2 x^{2} + 6 - 4 x^{2} = 0$

Step 1.4

Subtract $4 x^{2}$ from $- 2 x^{2}$ .

$- 6 x^{2} + 6 = 0$

Step 2

Subtract $6$ from both sides of the equation.

$- 6 x^{2} = - 6$

Step 3

Divide each term in $- 6 x^{2} = - 6$ by $- 6$ and simplify.

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Step 3.1

Divide each term in $- 6 x^{2} = - 6$ by $- 6$ .

$\frac{- 6 x^{2}}{- 6} = \frac{- 6}{- 6}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 6$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 6 x^{2}}{- 6} = \frac{- 6}{- 6}$

Step 3.2.1.2

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

$x^{2} = \frac{- 6}{- 6}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 6$ by $- 6$ .

$x^{2} = 1$

Step 4

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

$x = \pm \sqrt{1}$

Step 5

Any root of $1$ is $1$ .

$x = \pm 1$

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.

$x = 1$

Step 6.2

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

$x = - 1$

Step 6.3

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

$x = 1, - 1$