p^2+14p+27=0

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Solution for p^2+14p+27=0 equation:


Simplifying
p2 + 14p + 27 = 0

Reorder the terms:
27 + 14p + p2 = 0

Solving
27 + 14p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + 14p + -27 + p2 = 0 + -27

Reorder the terms:
27 + -27 + 14p + p2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + 14p + p2 = 0 + -27
14p + p2 = 0 + -27

Combine like terms: 0 + -27 = -27
14p + p2 = -27

The p term is 14p.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14p + 49 + p2 = -27 + 49

Reorder the terms:
49 + 14p + p2 = -27 + 49

Combine like terms: -27 + 49 = 22
49 + 14p + p2 = 22

Factor a perfect square on the left side:
(p + 7)(p + 7) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(p + 7) equal to 4.69041576 and -4.69041576.

Subproblem 1

p + 7 = 4.69041576 Simplifying p + 7 = 4.69041576 Reorder the terms: 7 + p = 4.69041576 Solving 7 + p = 4.69041576 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + p = 4.69041576 + -7 Combine like terms: 7 + -7 = 0 0 + p = 4.69041576 + -7 p = 4.69041576 + -7 Combine like terms: 4.69041576 + -7 = -2.30958424 p = -2.30958424 Simplifying p = -2.30958424

Subproblem 2

p + 7 = -4.69041576 Simplifying p + 7 = -4.69041576 Reorder the terms: 7 + p = -4.69041576 Solving 7 + p = -4.69041576 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + p = -4.69041576 + -7 Combine like terms: 7 + -7 = 0 0 + p = -4.69041576 + -7 p = -4.69041576 + -7 Combine like terms: -4.69041576 + -7 = -11.69041576 p = -11.69041576 Simplifying p = -11.69041576

Solution

The solution to the problem is based on the solutions from the subproblems. p = {-2.30958424, -11.69041576}

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