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Simplifying 7p2 + -12p = -4 Reorder the terms: -12p + 7p2 = -4 Solving -12p + 7p2 = -4 Solving for variable 'p'. Reorder the terms: 4 + -12p + 7p2 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + -12p + 7p2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.5714285714 + -1.714285714p + p2 = 0 Move the constant term to the right: Add '-0.5714285714' to each side of the equation. 0.5714285714 + -1.714285714p + -0.5714285714 + p2 = 0 + -0.5714285714 Reorder the terms: 0.5714285714 + -0.5714285714 + -1.714285714p + p2 = 0 + -0.5714285714 Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000 0.0000000000 + -1.714285714p + p2 = 0 + -0.5714285714 -1.714285714p + p2 = 0 + -0.5714285714 Combine like terms: 0 + -0.5714285714 = -0.5714285714 -1.714285714p + p2 = -0.5714285714 The p term is -1.714285714p. Take half its coefficient (-0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. -1.714285714p + 0.7346938773 + p2 = -0.5714285714 + 0.7346938773 Reorder the terms: 0.7346938773 + -1.714285714p + p2 = -0.5714285714 + 0.7346938773 Combine like terms: -0.5714285714 + 0.7346938773 = 0.1632653059 0.7346938773 + -1.714285714p + p2 = 0.1632653059 Factor a perfect square on the left side: (p + -0.857142857)(p + -0.857142857) = 0.1632653059 Calculate the square root of the right side: 0.404061018 Break this problem into two subproblems by setting (p + -0.857142857) equal to 0.404061018 and -0.404061018.Subproblem 1
p + -0.857142857 = 0.404061018 Simplifying p + -0.857142857 = 0.404061018 Reorder the terms: -0.857142857 + p = 0.404061018 Solving -0.857142857 + p = 0.404061018 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + p = 0.404061018 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + p = 0.404061018 + 0.857142857 p = 0.404061018 + 0.857142857 Combine like terms: 0.404061018 + 0.857142857 = 1.261203875 p = 1.261203875 Simplifying p = 1.261203875Subproblem 2
p + -0.857142857 = -0.404061018 Simplifying p + -0.857142857 = -0.404061018 Reorder the terms: -0.857142857 + p = -0.404061018 Solving -0.857142857 + p = -0.404061018 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + p = -0.404061018 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + p = -0.404061018 + 0.857142857 p = -0.404061018 + 0.857142857 Combine like terms: -0.404061018 + 0.857142857 = 0.453081839 p = 0.453081839 Simplifying p = 0.453081839Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.261203875, 0.453081839}
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