Finite Math Examples

$3 {(x + 8)}^{2} + 19 (x + 8) + 30$

Step 1

Set $3 {(x + 8)}^{2} + 19 (x + 8) + 30$ equal to $0$ .

$3 {(x + 8)}^{2} + 19 (x + 8) + 30 = 0$

Step 2

Simplify the left side.

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Step 2.1

Simplify $3 {(x + 8)}^{2} + 19 (x + 8) + 30$ .

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Apply the distributive property.

$3 {(x + 8)}^{2} + 19 x + 19 \cdot 8 + 30 = 0$

Step 2.1.1.2

Multiply $19$ by $8$ .

$3 {(x + 8)}^{2} + 19 x + 152 + 30 = 0$

Step 2.1.2

Add $152$ and $30$ .

$3 {(x + 8)}^{2} + 19 x + 182 = 0$

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 $a = 3$ , $b = 67$ , and $c = 374$ into the quadratic formula and solve for $x$ .

$\frac{- 67 \pm \sqrt{67^{2} - 4 \cdot (3 \cdot 374)}}{2 \cdot 3}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Raise $67$ to the power of $2$ .

$x = \frac{- 67 \pm \sqrt{4489 - 4 \cdot 3 \cdot 374}}{2 \cdot 3}$

Step 5.1.2

Multiply $- 4 \cdot 3 \cdot 374$ .

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Step 5.1.2.1

Multiply $- 4$ by $3$ .

$x = \frac{- 67 \pm \sqrt{4489 - 12 \cdot 374}}{2 \cdot 3}$

Step 5.1.2.2

Multiply $- 12$ by $374$ .

$x = \frac{- 67 \pm \sqrt{4489 - 4488}}{2 \cdot 3}$

Step 5.1.3

Subtract $4488$ from $4489$ .

$x = \frac{- 67 \pm \sqrt{1}}{2 \cdot 3}$

Step 5.1.4

Any root of $1$ is $1$ .

$x = \frac{- 67 \pm 1}{2 \cdot 3}$

Step 5.2

Multiply $2$ by $3$ .

$x = \frac{- 67 \pm 1}{6}$

Step 6

The final answer is the combination of both solutions.

$x = - 11, - \frac{34}{3}$