Get the solution to "How do you solve 0=p2−p−11?"

High School
Algebra
Algebra I
Quadratic function and equation

siutulysr5

Answered question

2022-01-20

How do you solve

0 = p^{2} - p - 11 ?

Answer & Explanation

shimmertulipsog

Beginner2022-01-21Added 10 answers

Step 1
If

a p^{2} + b p + c = 0

p = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

We have

a = 1, b = - 1, c = - 11

So:

p = \frac{1 \pm \sqrt{1 + 44}}{2} = \frac{1 \pm \sqrt{45}}{2}

= \frac{1 \pm \sqrt{3^{2} \times 5}}{2} = \frac{1 \pm 3 \sqrt{5}}{2}

Hence solutions are

p = \frac{1 \pm 3 \sqrt{5}}{2}

vasselefa

Beginner2022-01-22Added 9 answers

Step 1
$p^{2} - 2 p (\frac{1}{2}) + (\frac{1}{4}) - (11 + \frac{1}{4}) = 0$ or, ${(p - \frac{1}{2})}^{2} = \frac{45}{4}$
$= 5 {(\frac{3}{2})}^{2}$
or,
$[option 1] p - \frac{1}{2} = 3 \frac{\sqrt{5}}{2}$
or,
${(p - \frac{1}{2})}^{2} = \frac{45}{4}$
or,
$[option 2] p - \frac{1}{2} = - 3 \frac{\sqrt{5}}{2}$
or,
$p = \frac{1 - 3 \sqrt{5}}{2}$

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