Precalculus Examples

x^{2} + 30 x + 200 = 0

$x^{2} + 30 x + 200 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

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

Step 2

Substitute the values

a = 1

$a = 1$ ,

b = 30

$b = 30$ , and

c = 200

$c = 200$ into the quadratic formula and solve for

x

$x$ .

\frac{- 30 \pm \sqrt{30^{2} - 4 \cdot (1 \cdot 200)}}{2 \cdot 1}

$\frac{- 30 \pm \sqrt{30^{2} - 4 \cdot (1 \cdot 200)}}{2 \cdot 1}$

Step 3

Simplify.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Raise

30

$30$ to the power of

2

$2$ .

x = \frac{- 30 \pm \sqrt{900 - 4 \cdot 1 \cdot 200}}{2 \cdot 1}

$x = \frac{- 30 \pm \sqrt{900 - 4 \cdot 1 \cdot 200}}{2 \cdot 1}$

Step 3.1.2

Multiply

- 4 \cdot 1 \cdot 200

$- 4 \cdot 1 \cdot 200$ .

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Step 3.1.2.1

Multiply

- 4

$- 4$ by

1

$1$ .

x = \frac{- 30 \pm \sqrt{900 - 4 \cdot 200}}{2 \cdot 1}

$x = \frac{- 30 \pm \sqrt{900 - 4 \cdot 200}}{2 \cdot 1}$

Step 3.1.2.2

Multiply

- 4

$- 4$ by

200

$200$ .

x = \frac{- 30 \pm \sqrt{900 - 800}}{2 \cdot 1}

$x = \frac{- 30 \pm \sqrt{900 - 800}}{2 \cdot 1}$

x = \frac{- 30 \pm \sqrt{900 - 800}}{2 \cdot 1}

$x = \frac{- 30 \pm \sqrt{900 - 800}}{2 \cdot 1}$

Step 3.1.3

Subtract

800

$800$ from

900

$900$ .

x = \frac{- 30 \pm \sqrt{100}}{2 \cdot 1}

$x = \frac{- 30 \pm \sqrt{100}}{2 \cdot 1}$

Step 3.1.4

Rewrite

100

$100$ as

10^{2}

$10^{2}$ .

x = \frac{- 30 \pm \sqrt{10^{2}}}{2 \cdot 1}

$x = \frac{- 30 \pm \sqrt{10^{2}}}{2 \cdot 1}$

Step 3.1.5

Pull terms out from under the radical, assuming positive real numbers.

x = \frac{- 30 \pm 10}{2 \cdot 1}

$x = \frac{- 30 \pm 10}{2 \cdot 1}$

x = \frac{- 30 \pm 10}{2 \cdot 1}

$x = \frac{- 30 \pm 10}{2 \cdot 1}$

Step 3.2

Multiply

2

$2$ by

1

$1$ .

x = \frac{- 30 \pm 10}{2}

$x = \frac{- 30 \pm 10}{2}$

Step 3.3

Simplify

\frac{- 30 \pm 10}{2}

$\frac{- 30 \pm 10}{2}$ .

x = - 15 \pm 5

$x = - 15 \pm 5$

x = - 15 \pm 5

$x = - 15 \pm 5$

Step 4

The final answer is the combination of both solutions.

x = - 10, - 20

$x = - 10, - 20$