Basic Math Examples

$p = 250 p - 10200 - p^{2}$

Step 1

Since $p$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$250 p - 10200 - p^{2} = p$

Step 2

Move all terms containing $p$ to the left side of the equation.

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Step 2.1

Subtract $p$ from both sides of the equation.

$250 p - 10200 - p^{2} - p = 0$

Step 2.2

Subtract $p$ from $250 p$ .

$249 p - 10200 - p^{2} = 0$

Step 3

Use the quadratic formula to find the solutions.

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

Step 4

Substitute the values $a = - 1$ , $b = 249$ , and $c = - 10200$ into the quadratic formula and solve for $p$ .

$\frac{- 249 \pm \sqrt{249^{2} - 4 \cdot (- 1 \cdot - 10200)}}{2 \cdot - 1}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Raise $249$ to the power of $2$ .

$p = \frac{- 249 \pm \sqrt{62001 - 4 \cdot - 1 \cdot - 10200}}{2 \cdot - 1}$

Step 5.1.2

Multiply $- 4 \cdot - 1 \cdot - 10200$ .

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Step 5.1.2.1

Multiply $- 4$ by $- 1$ .

$p = \frac{- 249 \pm \sqrt{62001 + 4 \cdot - 10200}}{2 \cdot - 1}$

Step 5.1.2.2

Multiply $4$ by $- 10200$ .

$p = \frac{- 249 \pm \sqrt{62001 - 40800}}{2 \cdot - 1}$

Step 5.1.3

Subtract $40800$ from $62001$ .

$p = \frac{- 249 \pm \sqrt{21201}}{2 \cdot - 1}$

Step 5.2

Multiply $2$ by $- 1$ .

$p = \frac{- 249 \pm \sqrt{21201}}{- 2}$

Step 5.3

Simplify $\frac{- 249 \pm \sqrt{21201}}{- 2}$ .

$p = \frac{249 \pm \sqrt{21201}}{2}$

Step 6

The final answer is the combination of both solutions.

$p = \frac{249 + \sqrt{21201}}{2}, \frac{249 - \sqrt{21201}}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$p = \frac{249 + \sqrt{21201}}{2}, \frac{249 - \sqrt{21201}}{2}$

Decimal Form:

$p = 197.30281587 \dots, 51.69718412 \dots$