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Simplifying 7p2 + 2 = 12p Reorder the terms: 2 + 7p2 = 12p Solving 2 + 7p2 = 12p Solving for variable 'p'. Reorder the terms: 2 + -12p + 7p2 = 12p + -12p Combine like terms: 12p + -12p = 0 2 + -12p + 7p2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.2857142857 + -1.714285714p + p2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + -1.714285714p + -0.2857142857 + p2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + -1.714285714p + p2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + -1.714285714p + p2 = 0 + -0.2857142857 -1.714285714p + p2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 -1.714285714p + p2 = -0.2857142857 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 = -0.2857142857 + 0.7346938773 Reorder the terms: 0.7346938773 + -1.714285714p + p2 = -0.2857142857 + 0.7346938773 Combine like terms: -0.2857142857 + 0.7346938773 = 0.4489795916 0.7346938773 + -1.714285714p + p2 = 0.4489795916 Factor a perfect square on the left side: (p + -0.857142857)(p + -0.857142857) = 0.4489795916 Calculate the square root of the right side: 0.670059394 Break this problem into two subproblems by setting (p + -0.857142857) equal to 0.670059394 and -0.670059394.Subproblem 1
p + -0.857142857 = 0.670059394 Simplifying p + -0.857142857 = 0.670059394 Reorder the terms: -0.857142857 + p = 0.670059394 Solving -0.857142857 + p = 0.670059394 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 = 0.670059394 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + p = 0.670059394 + 0.857142857 p = 0.670059394 + 0.857142857 Combine like terms: 0.670059394 + 0.857142857 = 1.527202251 p = 1.527202251 Simplifying p = 1.527202251Subproblem 2
p + -0.857142857 = -0.670059394 Simplifying p + -0.857142857 = -0.670059394 Reorder the terms: -0.857142857 + p = -0.670059394 Solving -0.857142857 + p = -0.670059394 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 = -0.670059394 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + p = -0.670059394 + 0.857142857 p = -0.670059394 + 0.857142857 Combine like terms: -0.670059394 + 0.857142857 = 0.187083463 p = 0.187083463 Simplifying p = 0.187083463Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.527202251, 0.187083463}
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