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Simplifying 8p2 + -4p + -4 = 6p2 Reorder the terms: -4 + -4p + 8p2 = 6p2 Solving -4 + -4p + 8p2 = 6p2 Solving for variable 'p'. Combine like terms: 8p2 + -6p2 = 2p2 -4 + -4p + 2p2 = 6p2 + -6p2 Combine like terms: 6p2 + -6p2 = 0 -4 + -4p + 2p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -2p + p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -2p + p2)' equal to zero and attempt to solve: Simplifying -2 + -2p + p2 = 0 Solving -2 + -2p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -2p + 2 + p2 = 0 + 2 Reorder the terms: -2 + 2 + -2p + p2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2p + p2 = 0 + 2 -2p + p2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2p + p2 = 2 The p term is -2p. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2p + 1 + p2 = 2 + 1 Reorder the terms: 1 + -2p + p2 = 2 + 1 Combine like terms: 2 + 1 = 3 1 + -2p + p2 = 3 Factor a perfect square on the left side: (p + -1)(p + -1) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (p + -1) equal to 1.732050808 and -1.732050808.Subproblem 1
p + -1 = 1.732050808 Simplifying p + -1 = 1.732050808 Reorder the terms: -1 + p = 1.732050808 Solving -1 + p = 1.732050808 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + p = 1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + p = 1.732050808 + 1 p = 1.732050808 + 1 Combine like terms: 1.732050808 + 1 = 2.732050808 p = 2.732050808 Simplifying p = 2.732050808Subproblem 2
p + -1 = -1.732050808 Simplifying p + -1 = -1.732050808 Reorder the terms: -1 + p = -1.732050808 Solving -1 + p = -1.732050808 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + p = -1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + p = -1.732050808 + 1 p = -1.732050808 + 1 Combine like terms: -1.732050808 + 1 = -0.732050808 p = -0.732050808 Simplifying p = -0.732050808Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.732050808, -0.732050808}Solution
p = {2.732050808, -0.732050808}
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