Finite Math Examples

$x^{2} + 6 x + 3 = x - 6$

Step 1

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

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Step 1.1

Subtract $x$ from both sides of the equation.

$x^{2} + 6 x + 3 - x = - 6$

Step 1.2

Subtract $x$ from $6 x$ .

$x^{2} + 5 x + 3 = - 6$

Step 2

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

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Step 2.1

Add $6$ to both sides of the equation.

$x^{2} + 5 x + 3 + 6 = 0$

Step 2.2

Add $3$ and $6$ .

$x^{2} + 5 x + 9 = 0$

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 $a = 1$ , $b = 5$ , and $c = 9$ into the quadratic formula and solve for $x$ .

$\frac{- 5 \pm \sqrt{5^{2} - 4 \cdot (1 \cdot 9)}}{2 \cdot 1}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Raise $5$ to the power of $2$ .

$x = \frac{- 5 \pm \sqrt{25 - 4 \cdot 1 \cdot 9}}{2 \cdot 1}$

Step 5.1.2

Multiply $- 4 \cdot 1 \cdot 9$ .

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Step 5.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 5 \pm \sqrt{25 - 4 \cdot 9}}{2 \cdot 1}$

Step 5.1.2.2

Multiply $- 4$ by $9$ .

$x = \frac{- 5 \pm \sqrt{25 - 36}}{2 \cdot 1}$

Step 5.1.3

Subtract $36$ from $25$ .

$x = \frac{- 5 \pm \sqrt{- 11}}{2 \cdot 1}$

Step 5.1.4

Rewrite $- 11$ as $- 1 (11)$ .

$x = \frac{- 5 \pm \sqrt{- 1 \cdot 11}}{2 \cdot 1}$

Step 5.1.5

Rewrite $\sqrt{- 1 (11)}$ as $\sqrt{- 1} \cdot \sqrt{11}$ .

$x = \frac{- 5 \pm \sqrt{- 1} \cdot \sqrt{11}}{2 \cdot 1}$

Step 5.1.6

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{- 5 \pm i \sqrt{11}}{2 \cdot 1}$

Step 5.2

Multiply $2$ by $1$ .

$x = \frac{- 5 \pm i \sqrt{11}}{2}$

Step 6

The final answer is the combination of both solutions.

$x = - \frac{5 - i \sqrt{11}}{2}, - \frac{5 + i \sqrt{11}}{2}$