Precalculus Examples

$0 = - 0.025 x^{2} + x + 6$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Add $0.025 x^{2}$ to both sides of the equation.

$0.025 x^{2} = x + 6$

Step 1.2

Subtract $x$ from both sides of the equation.

$0.025 x^{2} - x = 6$

Step 1.3

Subtract $6$ from both sides of the equation.

$0.025 x^{2} - x - 6 = 0$

Step 2

Use the quadratic formula to find the solutions.

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

Step 3

Substitute the values $a = 0.025$ , $b = - 1$ , and $c = - 6$ into the quadratic formula and solve for $x$ .

$\frac{1 \pm \sqrt{{(- 1)}^{2} - 4 \cdot (0.025 \cdot - 6)}}{2 \cdot 0.025}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $- 1$ to the power of $2$ .

$x = \frac{1 \pm \sqrt{1 - 4 \cdot 0.025 \cdot - 6}}{2 \cdot 0.025}$

Step 4.1.2

Multiply $- 4 \cdot 0.025 \cdot - 6$ .

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Step 4.1.2.1

Multiply $- 4$ by $0.025$ .

$x = \frac{1 \pm \sqrt{1 - 0.1 \cdot - 6}}{2 \cdot 0.025}$

Step 4.1.2.2

Multiply $- 0.1$ by $- 6$ .

$x = \frac{1 \pm \sqrt{1 + 0.6}}{2 \cdot 0.025}$

Step 4.1.3

Add $1$ and $0.6$ .

$x = \frac{1 \pm \sqrt{1.6}}{2 \cdot 0.025}$

Step 4.2

Multiply $2$ by $0.025$ .

$x = \frac{1 \pm \sqrt{1.6}}{0.05}$

Step 4.3

Simplify $\frac{1 \pm \sqrt{1.6}}{0.05}$ .

$x = 20 \pm 25.29822128$

Step 5

The final answer is the combination of both solutions.

$x = 45.29822128, - 5.29822128$