Pre-Algebra Examples

$x^{2} + 2.9 x - 1610.9 = 0$

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 $a = 1$ , $b = 2.9$ , and $c = - 1610.9$ into the quadratic formula and solve for $x$ .

$\frac{- 2.9 \pm \sqrt{{2.9}^{2} - 4 \cdot (1 \cdot - 1610.9)}}{2 \cdot 1}$

Step 3

Simplify.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Raise $2.9$ to the power of $2$ .

$x = \frac{- 2.9 \pm \sqrt{8.41 - 4 \cdot 1 \cdot - 1610.9}}{2 \cdot 1}$

Step 3.1.2

Multiply $- 4 \cdot 1 \cdot - 1610.9$ .

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Step 3.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 2.9 \pm \sqrt{8.41 - 4 \cdot - 1610.9}}{2 \cdot 1}$

Step 3.1.2.2

Multiply $- 4$ by $- 1610.9$ .

$x = \frac{- 2.9 \pm \sqrt{8.41 + 6443.6}}{2 \cdot 1}$

Step 3.1.3

Add $8.41$ and $6443.6$ .

$x = \frac{- 2.9 \pm \sqrt{6452.01}}{2 \cdot 1}$

Step 3.2

Multiply $2$ by $1$ .

$x = \frac{- 2.9 \pm \sqrt{6452.01}}{2}$

Step 4

Simplify the expression to solve for the $+$ portion of the $\pm$ .

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $2.9$ to the power of $2$ .

$x = \frac{- 2.9 \pm \sqrt{8.41 - 4 \cdot 1 \cdot - 1610.9}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot - 1610.9$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 2.9 \pm \sqrt{8.41 - 4 \cdot - 1610.9}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $- 1610.9$ .

$x = \frac{- 2.9 \pm \sqrt{8.41 + 6443.6}}{2 \cdot 1}$

Step 4.1.3

Add $8.41$ and $6443.6$ .

$x = \frac{- 2.9 \pm \sqrt{6452.01}}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$x = \frac{- 2.9 \pm \sqrt{6452.01}}{2}$

Step 4.3

Change the $\pm$ to $+$ .

$x = \frac{- 2.9 + \sqrt{6452.01}}{2}$

Step 4.4

Add $- 2.9$ and $\sqrt{6452.01}$ .

$x = \frac{77.42440475}{2}$

Step 4.5

Divide $77.42440475$ by $2$ .

$x = 38.71220237$

Step 5

Simplify the expression to solve for the $-$ portion of the $\pm$ .

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Raise $2.9$ to the power of $2$ .

$x = \frac{- 2.9 \pm \sqrt{8.41 - 4 \cdot 1 \cdot - 1610.9}}{2 \cdot 1}$

Step 5.1.2

Multiply $- 4 \cdot 1 \cdot - 1610.9$ .

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Step 5.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 2.9 \pm \sqrt{8.41 - 4 \cdot - 1610.9}}{2 \cdot 1}$

Step 5.1.2.2

Multiply $- 4$ by $- 1610.9$ .

$x = \frac{- 2.9 \pm \sqrt{8.41 + 6443.6}}{2 \cdot 1}$

Step 5.1.3

Add $8.41$ and $6443.6$ .

$x = \frac{- 2.9 \pm \sqrt{6452.01}}{2 \cdot 1}$

Step 5.2

Multiply $2$ by $1$ .

$x = \frac{- 2.9 \pm \sqrt{6452.01}}{2}$

Step 5.3

Change the $\pm$ to $-$ .

$x = \frac{- 2.9 - \sqrt{6452.01}}{2}$

Step 5.4

Subtract $\sqrt{6452.01}$ from $- 2.9$ .

$x = \frac{- 83.22440475}{2}$

Step 5.5

Divide $- 83.22440475$ by $2$ .

$x = - 41.61220237$

Step 6

The final answer is the combination of both solutions.

$x = 38.71220237, - 41.61220237$