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Simplifying 2p2 = 7 + -12p Solving 2p2 = 7 + -12p Solving for variable 'p'. Reorder the terms: -7 + 12p + 2p2 = 7 + -12p + -7 + 12p Reorder the terms: -7 + 12p + 2p2 = 7 + -7 + -12p + 12p Combine like terms: 7 + -7 = 0 -7 + 12p + 2p2 = 0 + -12p + 12p -7 + 12p + 2p2 = -12p + 12p Combine like terms: -12p + 12p = 0 -7 + 12p + 2p2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 6p + p2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 6p + 3.5 + p2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 6p + p2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 6p + p2 = 0 + 3.5 6p + p2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 6p + p2 = 3.5 The p term is 6p. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6p + 9 + p2 = 3.5 + 9 Reorder the terms: 9 + 6p + p2 = 3.5 + 9 Combine like terms: 3.5 + 9 = 12.5 9 + 6p + p2 = 12.5 Factor a perfect square on the left side: (p + 3)(p + 3) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (p + 3) equal to 3.535533906 and -3.535533906.Subproblem 1
p + 3 = 3.535533906 Simplifying p + 3 = 3.535533906 Reorder the terms: 3 + p = 3.535533906 Solving 3 + p = 3.535533906 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = 3.535533906 + -3 Combine like terms: 3 + -3 = 0 0 + p = 3.535533906 + -3 p = 3.535533906 + -3 Combine like terms: 3.535533906 + -3 = 0.535533906 p = 0.535533906 Simplifying p = 0.535533906Subproblem 2
p + 3 = -3.535533906 Simplifying p + 3 = -3.535533906 Reorder the terms: 3 + p = -3.535533906 Solving 3 + p = -3.535533906 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = -3.535533906 + -3 Combine like terms: 3 + -3 = 0 0 + p = -3.535533906 + -3 p = -3.535533906 + -3 Combine like terms: -3.535533906 + -3 = -6.535533906 p = -6.535533906 Simplifying p = -6.535533906Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.535533906, -6.535533906}
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