Precalculus Examples

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

Step 1

Subtract $8$ from both sides of the equation.

$2 x^{2} + 5 x - 8 = 0$

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 $a = 2$ , $b = 5$ , and $c = - 8$ into the quadratic formula and solve for $x$ .

$\frac{- 5 \pm \sqrt{5^{2} - 4 \cdot (2 \cdot - 8)}}{2 \cdot 2}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

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

$x = \frac{- 5 \pm \sqrt{25 - 4 \cdot 2 \cdot - 8}}{2 \cdot 2}$

Step 4.1.2

Multiply $- 4 \cdot 2 \cdot - 8$ .

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Step 4.1.2.1

Multiply $- 4$ by $2$ .

$x = \frac{- 5 \pm \sqrt{25 - 8 \cdot - 8}}{2 \cdot 2}$

Step 4.1.2.2

Multiply $- 8$ by $- 8$ .

$x = \frac{- 5 \pm \sqrt{25 + 64}}{2 \cdot 2}$

Step 4.1.3

Add $25$ and $64$ .

$x = \frac{- 5 \pm \sqrt{89}}{2 \cdot 2}$

Step 4.2

Multiply $2$ by $2$ .

$x = \frac{- 5 \pm \sqrt{89}}{4}$

Step 5

The final answer is the combination of both solutions.

$x = - \frac{5 - \sqrt{89}}{4}, - \frac{5 + \sqrt{89}}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{5 - \sqrt{89}}{4}, - \frac{5 + \sqrt{89}}{4}$

Decimal Form:

$x = 1.10849528 \dots, - 3.60849528 \dots$