14=-p(p-8)

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Solution for 14=-p(p-8) equation:


Simplifying
14 = -1p(p + -8)

Reorder the terms:
14 = -1p(-8 + p)
14 = (-8 * -1p + p * -1p)
14 = (8p + -1p2)

Solving
14 = 8p + -1p2

Solving for variable 'p'.

Reorder the terms:
14 + -8p + p2 = 8p + -8p + -1p2 + p2

Combine like terms: 8p + -8p = 0
14 + -8p + p2 = 0 + -1p2 + p2
14 + -8p + p2 = -1p2 + p2

Combine like terms: -1p2 + p2 = 0
14 + -8p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + -8p + -14 + p2 = 0 + -14

Reorder the terms:
14 + -14 + -8p + p2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -8p + p2 = 0 + -14
-8p + p2 = 0 + -14

Combine like terms: 0 + -14 = -14
-8p + p2 = -14

The p term is -8p.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8p + 16 + p2 = -14 + 16

Reorder the terms:
16 + -8p + p2 = -14 + 16

Combine like terms: -14 + 16 = 2
16 + -8p + p2 = 2

Factor a perfect square on the left side:
(p + -4)(p + -4) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(p + -4) equal to 1.414213562 and -1.414213562.

Subproblem 1

p + -4 = 1.414213562 Simplifying p + -4 = 1.414213562 Reorder the terms: -4 + p = 1.414213562 Solving -4 + p = 1.414213562 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + p = 1.414213562 + 4 Combine like terms: -4 + 4 = 0 0 + p = 1.414213562 + 4 p = 1.414213562 + 4 Combine like terms: 1.414213562 + 4 = 5.414213562 p = 5.414213562 Simplifying p = 5.414213562

Subproblem 2

p + -4 = -1.414213562 Simplifying p + -4 = -1.414213562 Reorder the terms: -4 + p = -1.414213562 Solving -4 + p = -1.414213562 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + p = -1.414213562 + 4 Combine like terms: -4 + 4 = 0 0 + p = -1.414213562 + 4 p = -1.414213562 + 4 Combine like terms: -1.414213562 + 4 = 2.585786438 p = 2.585786438 Simplifying p = 2.585786438

Solution

The solution to the problem is based on the solutions from the subproblems. p = {5.414213562, 2.585786438}

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