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Simplifying 2p2 + -14p + 13 = 0 Reorder the terms: 13 + -14p + 2p2 = 0 Solving 13 + -14p + 2p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 6.5 + -7p + p2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + -7p + -6.5 + p2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + -7p + p2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + -7p + p2 = 0 + -6.5 -7p + p2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 -7p + p2 = -6.5 The p term is -7p. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7p + 12.25 + p2 = -6.5 + 12.25 Reorder the terms: 12.25 + -7p + p2 = -6.5 + 12.25 Combine like terms: -6.5 + 12.25 = 5.75 12.25 + -7p + p2 = 5.75 Factor a perfect square on the left side: (p + -3.5)(p + -3.5) = 5.75 Calculate the square root of the right side: 2.397915762 Break this problem into two subproblems by setting (p + -3.5) equal to 2.397915762 and -2.397915762.Subproblem 1
p + -3.5 = 2.397915762 Simplifying p + -3.5 = 2.397915762 Reorder the terms: -3.5 + p = 2.397915762 Solving -3.5 + p = 2.397915762 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + p = 2.397915762 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + p = 2.397915762 + 3.5 p = 2.397915762 + 3.5 Combine like terms: 2.397915762 + 3.5 = 5.897915762 p = 5.897915762 Simplifying p = 5.897915762Subproblem 2
p + -3.5 = -2.397915762 Simplifying p + -3.5 = -2.397915762 Reorder the terms: -3.5 + p = -2.397915762 Solving -3.5 + p = -2.397915762 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + p = -2.397915762 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + p = -2.397915762 + 3.5 p = -2.397915762 + 3.5 Combine like terms: -2.397915762 + 3.5 = 1.102084238 p = 1.102084238 Simplifying p = 1.102084238Solution
The solution to the problem is based on the solutions from the subproblems. p = {5.897915762, 1.102084238}
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