4p^2-20=12p

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Solution for 4p^2-20=12p equation:


Simplifying
4p2 + -20 = 12p

Reorder the terms:
-20 + 4p2 = 12p

Solving
-20 + 4p2 = 12p

Solving for variable 'p'.

Reorder the terms:
-20 + -12p + 4p2 = 12p + -12p

Combine like terms: 12p + -12p = 0
-20 + -12p + 4p2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + -3p + p2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-5 + -3p + p2)' equal to zero and attempt to solve: Simplifying -5 + -3p + p2 = 0 Solving -5 + -3p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -3p + 5 + p2 = 0 + 5 Reorder the terms: -5 + 5 + -3p + p2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3p + p2 = 0 + 5 -3p + p2 = 0 + 5 Combine like terms: 0 + 5 = 5 -3p + p2 = 5 The p term is -3p. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3p + 2.25 + p2 = 5 + 2.25 Reorder the terms: 2.25 + -3p + p2 = 5 + 2.25 Combine like terms: 5 + 2.25 = 7.25 2.25 + -3p + p2 = 7.25 Factor a perfect square on the left side: (p + -1.5)(p + -1.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (p + -1.5) equal to 2.692582404 and -2.692582404.

Subproblem 1

p + -1.5 = 2.692582404 Simplifying p + -1.5 = 2.692582404 Reorder the terms: -1.5 + p = 2.692582404 Solving -1.5 + p = 2.692582404 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + p = 2.692582404 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + p = 2.692582404 + 1.5 p = 2.692582404 + 1.5 Combine like terms: 2.692582404 + 1.5 = 4.192582404 p = 4.192582404 Simplifying p = 4.192582404

Subproblem 2

p + -1.5 = -2.692582404 Simplifying p + -1.5 = -2.692582404 Reorder the terms: -1.5 + p = -2.692582404 Solving -1.5 + p = -2.692582404 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + p = -2.692582404 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + p = -2.692582404 + 1.5 p = -2.692582404 + 1.5 Combine like terms: -2.692582404 + 1.5 = -1.192582404 p = -1.192582404 Simplifying p = -1.192582404

Solution

The solution to the problem is based on the solutions from the subproblems. p = {4.192582404, -1.192582404}

Solution

p = {4.192582404, -1.192582404}

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