Finite Math Examples

$21 - 11 x = 2 x^{2}$

Step 1

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

$21 - 11 x - 2 x^{2} = 0$

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 $a = - 2$ , $b = - 11$ , and $c = 21$ into the quadratic formula and solve for $x$ .

$\frac{11 \pm \sqrt{{(- 11)}^{2} - 4 \cdot (- 2 \cdot 21)}}{2 \cdot - 2}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $- 11$ to the power of $2$ .

$x = \frac{11 \pm \sqrt{121 - 4 \cdot - 2 \cdot 21}}{2 \cdot - 2}$

Step 4.1.2

Multiply $- 4 \cdot - 2 \cdot 21$ .

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Step 4.1.2.1

Multiply $- 4$ by $- 2$ .

$x = \frac{11 \pm \sqrt{121 + 8 \cdot 21}}{2 \cdot - 2}$

Step 4.1.2.2

Multiply $8$ by $21$ .

$x = \frac{11 \pm \sqrt{121 + 168}}{2 \cdot - 2}$

Step 4.1.3

Add $121$ and $168$ .

$x = \frac{11 \pm \sqrt{289}}{2 \cdot - 2}$

Step 4.1.4

Rewrite $289$ as $17^{2}$ .

$x = \frac{11 \pm \sqrt{17^{2}}}{2 \cdot - 2}$

Step 4.1.5

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

$x = \frac{11 \pm 17}{2 \cdot - 2}$

Step 4.2

Multiply $2$ by $- 2$ .

$x = \frac{11 \pm 17}{- 4}$

Step 4.3

Move the negative in front of the fraction.

$x = - \frac{11 \pm 17}{4}$

Step 5

The final answer is the combination of both solutions.

$x = - 7, \frac{3}{2}$