Algebra Examples

$7 x - 2 x = 5 x + 9 x + 12 + 8 + x^{2}$

Step 1

Move all terms to the left side of the equation and simplify.

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Step 1.1

Simplify the left side.

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Step 1.1.1

Subtract $2 x$ from $7 x$ .

$5 x = 5 x + 9 x + 12 + 8 + x^{2}$

Step 1.2

Simplify the right side.

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Step 1.2.1

Simplify $5 x + 9 x + 12 + 8 + x^{2}$ .

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Step 1.2.1.1

Add $5 x$ and $9 x$ .

$5 x = 14 x + 12 + 8 + x^{2}$

Step 1.2.1.2

Add $12$ and $8$ .

$5 x = 14 x + 20 + x^{2}$

Step 1.3

Move all the expressions to the left side of the equation.

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Step 1.3.1

Subtract $14 x$ from both sides of the equation.

$5 x - 14 x = 20 + x^{2}$

Step 1.3.2

Subtract $20$ from both sides of the equation.

$5 x - 14 x - 20 = x^{2}$

Step 1.3.3

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

$5 x - 14 x - 20 - x^{2} = 0$

Step 1.4

Subtract $14 x$ from $5 x$ .

$- 9 x - 20 - x^{2} = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = - 1$ , $b = - 9$ , and $c = - 20$ into the quadratic formula and solve for $x$ .

$\frac{9 \pm \sqrt{{(- 9)}^{2} - 4 \cdot (- 1 \cdot - 20)}}{2 \cdot - 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $- 9$ to the power of $2$ .

$x = \frac{9 \pm \sqrt{81 - 4 \cdot - 1 \cdot - 20}}{2 \cdot - 1}$

Step 4.1.2

Multiply $- 4 \cdot - 1 \cdot - 20$ .

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Step 4.1.2.1

Multiply $- 4$ by $- 1$ .

$x = \frac{9 \pm \sqrt{81 + 4 \cdot - 20}}{2 \cdot - 1}$

Step 4.1.2.2

Multiply $4$ by $- 20$ .

$x = \frac{9 \pm \sqrt{81 - 80}}{2 \cdot - 1}$

Step 4.1.3

Subtract $80$ from $81$ .

$x = \frac{9 \pm \sqrt{1}}{2 \cdot - 1}$

Step 4.1.4

Any root of $1$ is $1$ .

$x = \frac{9 \pm 1}{2 \cdot - 1}$

Step 4.2

Multiply $2$ by $- 1$ .

$x = \frac{9 \pm 1}{- 2}$

Step 4.3

Move the negative in front of the fraction.

$x = - \frac{9 \pm 1}{2}$

Step 5

The final answer is the combination of both solutions.

$x = - 5, - 4$