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Simplifying 4p2 + -7p = 3p + 2 Reorder the terms: -7p + 4p2 = 3p + 2 Reorder the terms: -7p + 4p2 = 2 + 3p Solving -7p + 4p2 = 2 + 3p Solving for variable 'p'. Reorder the terms: -2 + -7p + -3p + 4p2 = 2 + 3p + -2 + -3p Combine like terms: -7p + -3p = -10p -2 + -10p + 4p2 = 2 + 3p + -2 + -3p Reorder the terms: -2 + -10p + 4p2 = 2 + -2 + 3p + -3p Combine like terms: 2 + -2 = 0 -2 + -10p + 4p2 = 0 + 3p + -3p -2 + -10p + 4p2 = 3p + -3p Combine like terms: 3p + -3p = 0 -2 + -10p + 4p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -5p + 2p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -5p + 2p2)' equal to zero and attempt to solve: Simplifying -1 + -5p + 2p2 = 0 Solving -1 + -5p + 2p2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -2.5p + p2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -2.5p + 0.5 + p2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -2.5p + p2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -2.5p + p2 = 0 + 0.5 -2.5p + p2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -2.5p + p2 = 0.5 The p term is -2.5p. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5p + 1.5625 + p2 = 0.5 + 1.5625 Reorder the terms: 1.5625 + -2.5p + p2 = 0.5 + 1.5625 Combine like terms: 0.5 + 1.5625 = 2.0625 1.5625 + -2.5p + p2 = 2.0625 Factor a perfect square on the left side: (p + -1.25)(p + -1.25) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (p + -1.25) equal to 1.436140662 and -1.436140662.Subproblem 1
p + -1.25 = 1.436140662 Simplifying p + -1.25 = 1.436140662 Reorder the terms: -1.25 + p = 1.436140662 Solving -1.25 + p = 1.436140662 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + p = 1.436140662 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + p = 1.436140662 + 1.25 p = 1.436140662 + 1.25 Combine like terms: 1.436140662 + 1.25 = 2.686140662 p = 2.686140662 Simplifying p = 2.686140662Subproblem 2
p + -1.25 = -1.436140662 Simplifying p + -1.25 = -1.436140662 Reorder the terms: -1.25 + p = -1.436140662 Solving -1.25 + p = -1.436140662 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + p = -1.436140662 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + p = -1.436140662 + 1.25 p = -1.436140662 + 1.25 Combine like terms: -1.436140662 + 1.25 = -0.186140662 p = -0.186140662 Simplifying p = -0.186140662Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.686140662, -0.186140662}Solution
p = {2.686140662, -0.186140662}
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