Precalculus Examples

$97 = 215 x - 16 x^{2}$

Step 1

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

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Step 1.1

Subtract $215 x$ from both sides of the equation.

$97 - 215 x = - 16 x^{2}$

Step 1.2

Add $16 x^{2}$ to both sides of the equation.

$97 - 215 x + 16 x^{2} = 0$

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 $a = 16$ , $b = - 215$ , and $c = 97$ into the quadratic formula and solve for $x$ .

$\frac{215 \pm \sqrt{{(- 215)}^{2} - 4 \cdot (16 \cdot 97)}}{2 \cdot 16}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $- 215$ to the power of $2$ .

$x = \frac{215 \pm \sqrt{46225 - 4 \cdot 16 \cdot 97}}{2 \cdot 16}$

Step 4.1.2

Multiply $- 4 \cdot 16 \cdot 97$ .

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Step 4.1.2.1

Multiply $- 4$ by $16$ .

$x = \frac{215 \pm \sqrt{46225 - 64 \cdot 97}}{2 \cdot 16}$

Step 4.1.2.2

Multiply $- 64$ by $97$ .

$x = \frac{215 \pm \sqrt{46225 - 6208}}{2 \cdot 16}$

Step 4.1.3

Subtract $6208$ from $46225$ .

$x = \frac{215 \pm \sqrt{40017}}{2 \cdot 16}$

Step 4.2

Multiply $2$ by $16$ .

$x = \frac{215 \pm \sqrt{40017}}{32}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{215 \pm \sqrt{40017}}{32}$

Decimal Form:

$x = 12.97007798 \dots, 0.46742201 \dots$