Algebra Examples

$4 x^{2} + 9 x + 7 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = 4$ , $b = 9$ , and $c = 7$ into the quadratic formula and solve for $x$ .

$\frac{- 9 \pm \sqrt{9^{2} - 4 \cdot (4 \cdot 7)}}{2 \cdot 4}$

Step 3

Simplify.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

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

$x = \frac{- 9 \pm \sqrt{81 - 4 \cdot 4 \cdot 7}}{2 \cdot 4}$

Step 3.1.2

Multiply $- 4 \cdot 4 \cdot 7$ .

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Step 3.1.2.1

Multiply $- 4$ by $4$ .

$x = \frac{- 9 \pm \sqrt{81 - 16 \cdot 7}}{2 \cdot 4}$

Step 3.1.2.2

Multiply $- 16$ by $7$ .

$x = \frac{- 9 \pm \sqrt{81 - 112}}{2 \cdot 4}$

Step 3.1.3

Subtract $112$ from $81$ .

$x = \frac{- 9 \pm \sqrt{- 31}}{2 \cdot 4}$

Step 3.1.4

Rewrite $- 31$ as $- 1 (31)$ .

$x = \frac{- 9 \pm \sqrt{- 1 \cdot 31}}{2 \cdot 4}$

Step 3.1.5

Rewrite $\sqrt{- 1 (31)}$ as $\sqrt{- 1} \cdot \sqrt{31}$ .

$x = \frac{- 9 \pm \sqrt{- 1} \cdot \sqrt{31}}{2 \cdot 4}$

Step 3.1.6

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

$x = \frac{- 9 \pm i \sqrt{31}}{2 \cdot 4}$

Step 3.2

Multiply $2$ by $4$ .

$x = \frac{- 9 \pm i \sqrt{31}}{8}$