Algebra Examples

$p (x) = 5 (x^{2} + 1) + 16$

Step 1

Simplify $5 (x^{2} + 1) + 16$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$p x = 5 x^{2} + 5 \cdot 1 + 16$

Step 1.1.2

Multiply $5$ by $1$ .

$p x = 5 x^{2} + 5 + 16$

Step 1.2

Add $5$ and $16$ .

$p x = 5 x^{2} + 21$

Step 2

Subtract $5 x^{2}$ from both sides of the equation.

$p x - 5 x^{2} = 21$

Step 3

Subtract $21$ from both sides of the equation.

$p x - 5 x^{2} - 21 = 0$

Step 4

Use the quadratic formula to find the solutions.

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

Step 5

Substitute the values $a = - 5$ , $b = p$ , and $c = - 21$ into the quadratic formula and solve for $x$ .

$\frac{- p \pm \sqrt{p^{2} - 4 \cdot (- 5 \cdot - 21)}}{2 \cdot - 5}$

Step 6

Simplify.

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Step 6.1

Multiply $- 4 \cdot - 5 \cdot - 21$ .

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Step 6.1.1

Multiply $- 4$ by $- 5$ .

$x = \frac{- p \pm \sqrt{p^{2} + 20 \cdot - 21}}{2 \cdot - 5}$

Step 6.1.2

Multiply $20$ by $- 21$ .

$x = \frac{- p \pm \sqrt{p^{2} - 420}}{2 \cdot - 5}$

Step 6.2

Multiply $2$ by $- 5$ .

$x = \frac{- p \pm \sqrt{p^{2} - 420}}{- 10}$

Step 6.3

Simplify $\frac{- p \pm \sqrt{p^{2} - 420}}{- 10}$ .

$x = \frac{p \pm \sqrt{p^{2} - 420}}{10}$

Step 7

The final answer is the combination of both solutions.

$x = \frac{p + \sqrt{p^{2} - 420}}{10}$

$x = \frac{p - \sqrt{p^{2} - 420}}{10}$