Finite Math Examples

$0 = 0.5 x^{2} + 1.5 x + 6.87$

Step 1

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

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Step 1.1

Subtract $0.5 x^{2}$ from both sides of the equation.

$- 0.5 x^{2} = 1.5 x + 6.87$

Step 1.2

Subtract $1.5 x$ from both sides of the equation.

$- 0.5 x^{2} - 1.5 x = 6.87$

Step 1.3

Subtract $6.87$ from both sides of the equation.

$- 0.5 x^{2} - 1.5 x - 6.87 = 0$

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 $a = - 0.5$ , $b = - 1.5$ , and $c = - 6.87$ into the quadratic formula and solve for $x$ .

$\frac{1.5 \pm \sqrt{{(- 1.5)}^{2} - 4 \cdot (- 0.5 \cdot - 6.87)}}{2 \cdot - 0.5}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $- 1.5$ to the power of $2$ .

$x = \frac{1.5 \pm \sqrt{2.25 - 4 \cdot - 0.5 \cdot - 6.87}}{2 \cdot - 0.5}$

Step 4.1.2

Multiply $- 4 \cdot - 0.5 \cdot - 6.87$ .

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Step 4.1.2.1

Multiply $- 4$ by $- 0.5$ .

$x = \frac{1.5 \pm \sqrt{2.25 + 2 \cdot - 6.87}}{2 \cdot - 0.5}$

Step 4.1.2.2

Multiply $2$ by $- 6.87$ .

$x = \frac{1.5 \pm \sqrt{2.25 - 13.74}}{2 \cdot - 0.5}$

Step 4.1.3

Subtract $13.74$ from $2.25$ .

$x = \frac{1.5 \pm \sqrt{- 11.49}}{2 \cdot - 0.5}$

Step 4.1.4

Rewrite $- 11.49$ as $- 1 (11.49)$ .

$x = \frac{1.5 \pm \sqrt{- 1 \cdot 11.49}}{2 \cdot - 0.5}$

Step 4.1.5

Rewrite $\sqrt{- 1 (11.49)}$ as $\sqrt{- 1} \cdot \sqrt{11.49}$ .

$x = \frac{1.5 \pm \sqrt{- 1} \cdot \sqrt{11.49}}{2 \cdot - 0.5}$

Step 4.1.6

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

$x = \frac{1.5 \pm i \sqrt{11.49}}{2 \cdot - 0.5}$

Step 4.2

Multiply $2$ by $- 0.5$ .

$x = \frac{1.5 \pm i \sqrt{11.49}}{- 1}$

Step 4.3

Move the negative one from the denominator of $\frac{1.5 \pm i \sqrt{11.49}}{- 1}$ .

$x = - 1 \cdot (1.5 \pm i \sqrt{11.49})$

Step 4.4

Rewrite $- 1 \cdot (1.5 \pm i \sqrt{11.49})$ as $- (1.5 \pm i \sqrt{11.49})$ .

$x = - (1.5 \pm i \sqrt{11.49})$