Algebra Examples

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

Step 1

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

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Step 1.1

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

$- 5 x^{2} - 9 x - x^{2} = 2 x - 8$

Step 1.2

Subtract $2 x$ from both sides of the equation.

$- 5 x^{2} - 9 x - x^{2} - 2 x = - 8$

Step 1.3

Subtract $x^{2}$ from $- 5 x^{2}$ .

$- 6 x^{2} - 9 x - 2 x = - 8$

Step 1.4

Subtract $2 x$ from $- 9 x$ .

$- 6 x^{2} - 11 x = - 8$

Step 2

Add $8$ to both sides of the equation.

$- 6 x^{2} - 11 x + 8 = 0$

Step 3

Use the quadratic formula to find the solutions.

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

Step 4

Substitute the values $a = - 6$ , $b = - 11$ , and $c = 8$ into the quadratic formula and solve for $x$ .

$\frac{11 \pm \sqrt{{(- 11)}^{2} - 4 \cdot (- 6 \cdot 8)}}{2 \cdot - 6}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Raise $- 11$ to the power of $2$ .

$x = \frac{11 \pm \sqrt{121 - 4 \cdot - 6 \cdot 8}}{2 \cdot - 6}$

Step 5.1.2

Multiply $- 4 \cdot - 6 \cdot 8$ .

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Step 5.1.2.1

Multiply $- 4$ by $- 6$ .

$x = \frac{11 \pm \sqrt{121 + 24 \cdot 8}}{2 \cdot - 6}$

Step 5.1.2.2

Multiply $24$ by $8$ .

$x = \frac{11 \pm \sqrt{121 + 192}}{2 \cdot - 6}$

Step 5.1.3

Add $121$ and $192$ .

$x = \frac{11 \pm \sqrt{313}}{2 \cdot - 6}$

Step 5.2

Multiply $2$ by $- 6$ .

$x = \frac{11 \pm \sqrt{313}}{- 12}$

Step 5.3

Move the negative in front of the fraction.

$x = - \frac{11 \pm \sqrt{313}}{12}$

Step 6

The final answer is the combination of both solutions.

$x = - \frac{11 + \sqrt{313}}{12}, - \frac{11 - \sqrt{313}}{12}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{11 + \sqrt{313}}{12}, - \frac{11 - \sqrt{313}}{12}$

Decimal Form:

$x = - 2.39098383 \dots, 0.55765050 \dots$