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Simplifying 6p + -6 = p2 Reorder the terms: -6 + 6p = p2 Solving -6 + 6p = p2 Solving for variable 'p'. Combine like terms: p2 + -1p2 = 0 -6 + 6p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 6 + -6p + p2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -6p + -6 + p2 = 0 + -6 Reorder the terms: 6 + -6 + -6p + p2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -6p + p2 = 0 + -6 -6p + p2 = 0 + -6 Combine like terms: 0 + -6 = -6 -6p + p2 = -6 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 = -6 + 9 Reorder the terms: 9 + -6p + p2 = -6 + 9 Combine like terms: -6 + 9 = 3 9 + -6p + p2 = 3 Factor a perfect square on the left side: (p + -3)(p + -3) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (p + -3) equal to 1.732050808 and -1.732050808.Subproblem 1
p + -3 = 1.732050808 Simplifying p + -3 = 1.732050808 Reorder the terms: -3 + p = 1.732050808 Solving -3 + p = 1.732050808 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 = 1.732050808 + 3 Combine like terms: -3 + 3 = 0 0 + p = 1.732050808 + 3 p = 1.732050808 + 3 Combine like terms: 1.732050808 + 3 = 4.732050808 p = 4.732050808 Simplifying p = 4.732050808Subproblem 2
p + -3 = -1.732050808 Simplifying p + -3 = -1.732050808 Reorder the terms: -3 + p = -1.732050808 Solving -3 + p = -1.732050808 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 = -1.732050808 + 3 Combine like terms: -3 + 3 = 0 0 + p = -1.732050808 + 3 p = -1.732050808 + 3 Combine like terms: -1.732050808 + 3 = 1.267949192 p = 1.267949192 Simplifying p = 1.267949192Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.732050808, 1.267949192}
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