Algebra Examples

$- 4 x^{2} - 40 x - 280 = 0$

Step 1

Factor $- 4$ out of $- 4 x^{2} - 40 x - 280$ .

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Step 1.1

Factor $- 4$ out of $- 4 x^{2}$ .

$- 4 x^{2} - 40 x - 280 = 0$

Step 1.2

Factor $- 4$ out of $- 40 x$ .

$- 4 x^{2} - 4 (10 x) - 280 = 0$

Step 1.3

Factor $- 4$ out of $- 280$ .

$- 4 x^{2} - 4 (10 x) - 4 \cdot 70 = 0$

Step 1.4

Factor $- 4$ out of $- 4 (x^{2}) - 4 (10 x)$ .

$- 4 (x^{2} + 10 x) - 4 \cdot 70 = 0$

Step 1.5

Factor $- 4$ out of $- 4 (x^{2} + 10 x) - 4 (70)$ .

$- 4 (x^{2} + 10 x + 70) = 0$

Step 2

Divide each term in $- 4 (x^{2} + 10 x + 70) = 0$ by $- 4$ and simplify.

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Step 2.1

Divide each term in $- 4 (x^{2} + 10 x + 70) = 0$ by $- 4$ .

$\frac{- 4 (x^{2} + 10 x + 70)}{- 4} = \frac{0}{- 4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 4 (x^{2} + 10 x + 70)}{- 4} = \frac{0}{- 4}$

Step 2.2.1.2

Divide $x^{2} + 10 x + 70$ by $1$ .

$x^{2} + 10 x + 70 = \frac{0}{- 4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $0$ by $- 4$ .

$x^{2} + 10 x + 70 = 0$

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 $a = 1$ , $b = 10$ , and $c = 70$ into the quadratic formula and solve for $x$ .

$\frac{- 10 \pm \sqrt{10^{2} - 4 \cdot (1 \cdot 70)}}{2 \cdot 1}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Raise $10$ to the power of $2$ .

$x = \frac{- 10 \pm \sqrt{100 - 4 \cdot 1 \cdot 70}}{2 \cdot 1}$

Step 5.1.2

Multiply $- 4 \cdot 1 \cdot 70$ .

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Step 5.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 10 \pm \sqrt{100 - 4 \cdot 70}}{2 \cdot 1}$

Step 5.1.2.2

Multiply $- 4$ by $70$ .

$x = \frac{- 10 \pm \sqrt{100 - 280}}{2 \cdot 1}$

Step 5.1.3

Subtract $280$ from $100$ .

$x = \frac{- 10 \pm \sqrt{- 180}}{2 \cdot 1}$

Step 5.1.4

Rewrite $- 180$ as $- 1 (180)$ .

$x = \frac{- 10 \pm \sqrt{- 1 \cdot 180}}{2 \cdot 1}$

Step 5.1.5

Rewrite $\sqrt{- 1 (180)}$ as $\sqrt{- 1} \cdot \sqrt{180}$ .

$x = \frac{- 10 \pm \sqrt{- 1} \cdot \sqrt{180}}{2 \cdot 1}$

Step 5.1.6

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

$x = \frac{- 10 \pm i \cdot \sqrt{180}}{2 \cdot 1}$

Step 5.1.7

Rewrite $180$ as $6^{2} \cdot 5$ .

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Step 5.1.7.1

Factor $36$ out of $180$ .

$x = \frac{- 10 \pm i \cdot \sqrt{36 (5)}}{2 \cdot 1}$

Step 5.1.7.2

Rewrite $36$ as $6^{2}$ .

$x = \frac{- 10 \pm i \cdot \sqrt{6^{2} \cdot 5}}{2 \cdot 1}$

Step 5.1.8

Pull terms out from under the radical.

$x = \frac{- 10 \pm i \cdot (6 \sqrt{5})}{2 \cdot 1}$

Step 5.1.9

Move $6$ to the left of $i$ .

$x = \frac{- 10 \pm 6 i \sqrt{5}}{2 \cdot 1}$

Step 5.2

Multiply $2$ by $1$ .

$x = \frac{- 10 \pm 6 i \sqrt{5}}{2}$

Step 5.3

Simplify $\frac{- 10 \pm 6 i \sqrt{5}}{2}$ .

$x = - 5 \pm 3 i \sqrt{5}$

Step 6