Finite Math Examples

$p x^{2} - x - 56 p = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = p$ , $b = - 1$ , and $c = - 56 p$ into the quadratic formula and solve for $x$ .

$\frac{1 \pm \sqrt{{(- 1)}^{2} - 4 \cdot (p \cdot (- 56 p))}}{2 p}$

Step 3

Simplify the numerator.

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Step 3.1

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

$x = \frac{1 \pm \sqrt{1 - 4 \cdot p \cdot (- 56 p)}}{2 p}$

Step 3.2

Rewrite using the commutative property of multiplication.

$x = \frac{1 \pm \sqrt{1 - 4 \cdot (- 56 p \cdot p)}}{2 p}$

Step 3.3

Multiply $p$ by $p$ by adding the exponents.

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Step 3.3.1

Move $p$ .

$x = \frac{1 \pm \sqrt{1 - 4 \cdot (- 56 (p \cdot p))}}{2 p}$

Step 3.3.2

Multiply $p$ by $p$ .

$x = \frac{1 \pm \sqrt{1 - 4 \cdot (- 56 p^{2})}}{2 p}$

Step 3.4

Multiply $- 4$ by $- 56$ .

$x = \frac{1 \pm \sqrt{1 + 224 p^{2}}}{2 p}$

Step 4

The final answer is the combination of both solutions.

$x = \frac{1 + \sqrt{1 + 224 p^{2}}}{2 p}$

$x = \frac{1 - \sqrt{1 + 224 p^{2}}}{2 p}$