4p^2-56=-16p

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Solution for 4p^2-56=-16p equation:


Simplifying
4p2 + -56 = -16p

Reorder the terms:
-56 + 4p2 = -16p

Solving
-56 + 4p2 = -16p

Solving for variable 'p'.

Reorder the terms:
-56 + 16p + 4p2 = -16p + 16p

Combine like terms: -16p + 16p = 0
-56 + 16p + 4p2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-14 + 4p + p2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-14 + 4p + p2)' equal to zero and attempt to solve: Simplifying -14 + 4p + p2 = 0 Solving -14 + 4p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 4p + 14 + p2 = 0 + 14 Reorder the terms: -14 + 14 + 4p + p2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 4p + p2 = 0 + 14 4p + p2 = 0 + 14 Combine like terms: 0 + 14 = 14 4p + p2 = 14 The p term is 4p. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4p + 4 + p2 = 14 + 4 Reorder the terms: 4 + 4p + p2 = 14 + 4 Combine like terms: 14 + 4 = 18 4 + 4p + p2 = 18 Factor a perfect square on the left side: (p + 2)(p + 2) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (p + 2) equal to 4.242640687 and -4.242640687.

Subproblem 1

p + 2 = 4.242640687 Simplifying p + 2 = 4.242640687 Reorder the terms: 2 + p = 4.242640687 Solving 2 + p = 4.242640687 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = 4.242640687 + -2 Combine like terms: 2 + -2 = 0 0 + p = 4.242640687 + -2 p = 4.242640687 + -2 Combine like terms: 4.242640687 + -2 = 2.242640687 p = 2.242640687 Simplifying p = 2.242640687

Subproblem 2

p + 2 = -4.242640687 Simplifying p + 2 = -4.242640687 Reorder the terms: 2 + p = -4.242640687 Solving 2 + p = -4.242640687 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = -4.242640687 + -2 Combine like terms: 2 + -2 = 0 0 + p = -4.242640687 + -2 p = -4.242640687 + -2 Combine like terms: -4.242640687 + -2 = -6.242640687 p = -6.242640687 Simplifying p = -6.242640687

Solution

The solution to the problem is based on the solutions from the subproblems. p = {2.242640687, -6.242640687}

Solution

p = {2.242640687, -6.242640687}

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