Finite Math Examples

$x (x + 16) = 2240$

Step 1

Move all terms to the left side of the equation and simplify.

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Step 1.1

Simplify the left side.

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Step 1.1.1

Simplify $x (x + 16)$ .

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Step 1.1.1.1

Apply the distributive property.

$x \cdot x + x \cdot 16 = 2240$

Step 1.1.1.2

Simplify the expression.

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Step 1.1.1.2.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot 16 = 2240$

Step 1.1.1.2.2

Move $16$ to the left of $x$ .

$x^{2} + 16 x = 2240$

Step 1.2

Subtract $2240$ from both sides of the equation.

$x^{2} + 16 x - 2240 = 0$

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 $a = 1$ , $b = 16$ , and $c = - 2240$ into the quadratic formula and solve for $x$ .

$\frac{- 16 \pm \sqrt{16^{2} - 4 \cdot (1 \cdot - 2240)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $16$ to the power of $2$ .

$x = \frac{- 16 \pm \sqrt{256 - 4 \cdot 1 \cdot - 2240}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot - 2240$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 16 \pm \sqrt{256 - 4 \cdot - 2240}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $- 2240$ .

$x = \frac{- 16 \pm \sqrt{256 + 8960}}{2 \cdot 1}$

Step 4.1.3

Add $256$ and $8960$ .

$x = \frac{- 16 \pm \sqrt{9216}}{2 \cdot 1}$

Step 4.1.4

Rewrite $9216$ as $96^{2}$ .

$x = \frac{- 16 \pm \sqrt{96^{2}}}{2 \cdot 1}$

Step 4.1.5

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

$x = \frac{- 16 \pm 96}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$x = \frac{- 16 \pm 96}{2}$

Step 4.3

Simplify $\frac{- 16 \pm 96}{2}$ .

$x = - 8 \pm 48$

Step 5

The final answer is the combination of both solutions.

$x = 40, - 56$