Pre-Algebra Examples

$- 35 x = 17 + 5 x^{2}$

Step 1

Subtract $5 x^{2}$ from both sides of the equation.

$- 35 x - 5 x^{2} = 17$

Step 2

Subtract $17$ from both sides of the equation.

$- 35 x - 5 x^{2} - 17 = 0$

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 $a = - 5$ , $b = - 35$ , and $c = - 17$ into the quadratic formula and solve for $x$ .

$\frac{35 \pm \sqrt{{(- 35)}^{2} - 4 \cdot (- 5 \cdot - 17)}}{2 \cdot - 5}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Raise $- 35$ to the power of $2$ .

$x = \frac{35 \pm \sqrt{1225 - 4 \cdot - 5 \cdot - 17}}{2 \cdot - 5}$

Step 5.1.2

Multiply $- 4 \cdot - 5 \cdot - 17$ .

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Step 5.1.2.1

Multiply $- 4$ by $- 5$ .

$x = \frac{35 \pm \sqrt{1225 + 20 \cdot - 17}}{2 \cdot - 5}$

Step 5.1.2.2

Multiply $20$ by $- 17$ .

$x = \frac{35 \pm \sqrt{1225 - 340}}{2 \cdot - 5}$

Step 5.1.3

Subtract $340$ from $1225$ .

$x = \frac{35 \pm \sqrt{885}}{2 \cdot - 5}$

Step 5.2

Multiply $2$ by $- 5$ .

$x = \frac{35 \pm \sqrt{885}}{- 10}$

Step 5.3

Move the negative in front of the fraction.

$x = - \frac{35 \pm \sqrt{885}}{10}$

Step 6

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

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Raise $- 35$ to the power of $2$ .

$x = \frac{35 \pm \sqrt{1225 - 4 \cdot - 5 \cdot - 17}}{2 \cdot - 5}$

Step 6.1.2

Multiply $- 4 \cdot - 5 \cdot - 17$ .

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Step 6.1.2.1

Multiply $- 4$ by $- 5$ .

$x = \frac{35 \pm \sqrt{1225 + 20 \cdot - 17}}{2 \cdot - 5}$

Step 6.1.2.2

Multiply $20$ by $- 17$ .

$x = \frac{35 \pm \sqrt{1225 - 340}}{2 \cdot - 5}$

Step 6.1.3

Subtract $340$ from $1225$ .

$x = \frac{35 \pm \sqrt{885}}{2 \cdot - 5}$

Step 6.2

Multiply $2$ by $- 5$ .

$x = \frac{35 \pm \sqrt{885}}{- 10}$

Step 6.3

Move the negative in front of the fraction.

$x = - \frac{35 \pm \sqrt{885}}{10}$

Step 6.4

Change the $\pm$ to $+$ .

$x = - \frac{35 + \sqrt{885}}{10}$

Step 7

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

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Step 7.1

Simplify the numerator.

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Step 7.1.1

Raise $- 35$ to the power of $2$ .

$x = \frac{35 \pm \sqrt{1225 - 4 \cdot - 5 \cdot - 17}}{2 \cdot - 5}$

Step 7.1.2

Multiply $- 4 \cdot - 5 \cdot - 17$ .

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Step 7.1.2.1

Multiply $- 4$ by $- 5$ .

$x = \frac{35 \pm \sqrt{1225 + 20 \cdot - 17}}{2 \cdot - 5}$

Step 7.1.2.2

Multiply $20$ by $- 17$ .

$x = \frac{35 \pm \sqrt{1225 - 340}}{2 \cdot - 5}$

Step 7.1.3

Subtract $340$ from $1225$ .

$x = \frac{35 \pm \sqrt{885}}{2 \cdot - 5}$

Step 7.2

Multiply $2$ by $- 5$ .

$x = \frac{35 \pm \sqrt{885}}{- 10}$

Step 7.3

Move the negative in front of the fraction.

$x = - \frac{35 \pm \sqrt{885}}{10}$

Step 7.4

Change the $\pm$ to $-$ .

$x = - \frac{35 - \sqrt{885}}{10}$

Step 8

The final answer is the combination of both solutions.

$x = - \frac{35 + \sqrt{885}}{10}, - \frac{35 - \sqrt{885}}{10}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{35 + \sqrt{885}}{10}, - \frac{35 - \sqrt{885}}{10}$

Decimal Form:

$x = - 6.47489495 \dots, - 0.52510504 \dots$