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Simplifying 3p2 + -15p + 7 = 0 Reorder the terms: 7 + -15p + 3p2 = 0 Solving 7 + -15p + 3p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.333333333 + -5p + p2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + -5p + -2.333333333 + p2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + -5p + p2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + -5p + p2 = 0 + -2.333333333 -5p + p2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 -5p + p2 = -2.333333333 The p term is -5p. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5p + 6.25 + p2 = -2.333333333 + 6.25 Reorder the terms: 6.25 + -5p + p2 = -2.333333333 + 6.25 Combine like terms: -2.333333333 + 6.25 = 3.916666667 6.25 + -5p + p2 = 3.916666667 Factor a perfect square on the left side: (p + -2.5)(p + -2.5) = 3.916666667 Calculate the square root of the right side: 1.979057015 Break this problem into two subproblems by setting (p + -2.5) equal to 1.979057015 and -1.979057015.Subproblem 1
p + -2.5 = 1.979057015 Simplifying p + -2.5 = 1.979057015 Reorder the terms: -2.5 + p = 1.979057015 Solving -2.5 + p = 1.979057015 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + p = 1.979057015 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + p = 1.979057015 + 2.5 p = 1.979057015 + 2.5 Combine like terms: 1.979057015 + 2.5 = 4.479057015 p = 4.479057015 Simplifying p = 4.479057015Subproblem 2
p + -2.5 = -1.979057015 Simplifying p + -2.5 = -1.979057015 Reorder the terms: -2.5 + p = -1.979057015 Solving -2.5 + p = -1.979057015 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + p = -1.979057015 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + p = -1.979057015 + 2.5 p = -1.979057015 + 2.5 Combine like terms: -1.979057015 + 2.5 = 0.520942985 p = 0.520942985 Simplifying p = 0.520942985Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.479057015, 0.520942985}
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