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Simplifying 3p = p2 + -12 Reorder the terms: 3p = -12 + p2 Solving 3p = -12 + p2 Solving for variable 'p'. Reorder the terms: 12 + 3p + -1p2 = -12 + p2 + 12 + -1p2 Reorder the terms: 12 + 3p + -1p2 = -12 + 12 + p2 + -1p2 Combine like terms: -12 + 12 = 0 12 + 3p + -1p2 = 0 + p2 + -1p2 12 + 3p + -1p2 = p2 + -1p2 Combine like terms: p2 + -1p2 = 0 12 + 3p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -12 + -3p + p2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -3p + 12 + p2 = 0 + 12 Reorder the terms: -12 + 12 + -3p + p2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -3p + p2 = 0 + 12 -3p + p2 = 0 + 12 Combine like terms: 0 + 12 = 12 -3p + p2 = 12 The p term is -3p. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3p + 2.25 + p2 = 12 + 2.25 Reorder the terms: 2.25 + -3p + p2 = 12 + 2.25 Combine like terms: 12 + 2.25 = 14.25 2.25 + -3p + p2 = 14.25 Factor a perfect square on the left side: (p + -1.5)(p + -1.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (p + -1.5) equal to 3.774917218 and -3.774917218.Subproblem 1
p + -1.5 = 3.774917218 Simplifying p + -1.5 = 3.774917218 Reorder the terms: -1.5 + p = 3.774917218 Solving -1.5 + p = 3.774917218 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + p = 3.774917218 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + p = 3.774917218 + 1.5 p = 3.774917218 + 1.5 Combine like terms: 3.774917218 + 1.5 = 5.274917218 p = 5.274917218 Simplifying p = 5.274917218Subproblem 2
p + -1.5 = -3.774917218 Simplifying p + -1.5 = -3.774917218 Reorder the terms: -1.5 + p = -3.774917218 Solving -1.5 + p = -3.774917218 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + p = -3.774917218 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + p = -3.774917218 + 1.5 p = -3.774917218 + 1.5 Combine like terms: -3.774917218 + 1.5 = -2.274917218 p = -2.274917218 Simplifying p = -2.274917218Solution
The solution to the problem is based on the solutions from the subproblems. p = {5.274917218, -2.274917218}
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