p^2+5p=14

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Solution for p^2+5p=14 equation:


Simplifying
p2 + 5p = 14

Reorder the terms:
5p + p2 = 14

Solving
5p + p2 = 14

Solving for variable 'p'.

Reorder the terms:
-14 + 5p + p2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + 5p + p2 = 0

Factor a trinomial.
(-7 + -1p)(2 + -1p) = 0

Subproblem 1

Set the factor '(-7 + -1p)' equal to zero and attempt to solve: Simplifying -7 + -1p = 0 Solving -7 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1p = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1p = 0 + 7 -1p = 0 + 7 Combine like terms: 0 + 7 = 7 -1p = 7 Divide each side by '-1'. p = -7 Simplifying p = -7

Subproblem 2

Set the factor '(2 + -1p)' equal to zero and attempt to solve: Simplifying 2 + -1p = 0 Solving 2 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1p = 0 + -2 -1p = 0 + -2 Combine like terms: 0 + -2 = -2 -1p = -2 Divide each side by '-1'. p = 2 Simplifying p = 2

Solution

p = {-7, 2}

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