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Simplifying -3p2 = 12p + 8 Reorder the terms: -3p2 = 8 + 12p Solving -3p2 = 8 + 12p Solving for variable 'p'. Reorder the terms: -8 + -12p + -3p2 = 8 + 12p + -8 + -12p Reorder the terms: -8 + -12p + -3p2 = 8 + -8 + 12p + -12p Combine like terms: 8 + -8 = 0 -8 + -12p + -3p2 = 0 + 12p + -12p -8 + -12p + -3p2 = 12p + -12p Combine like terms: 12p + -12p = 0 -8 + -12p + -3p2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 12p + 3p2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 12p + 3p2)' equal to zero and attempt to solve: Simplifying 8 + 12p + 3p2 = 0 Solving 8 + 12p + 3p2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.666666667 + 4p + p2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + 4p + -2.666666667 + p2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + 4p + p2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + 4p + p2 = 0 + -2.666666667 4p + p2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 4p + p2 = -2.666666667 The p term is 4p. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4p + 4 + p2 = -2.666666667 + 4 Reorder the terms: 4 + 4p + p2 = -2.666666667 + 4 Combine like terms: -2.666666667 + 4 = 1.333333333 4 + 4p + p2 = 1.333333333 Factor a perfect square on the left side: (p + 2)(p + 2) = 1.333333333 Calculate the square root of the right side: 1.154700538 Break this problem into two subproblems by setting (p + 2) equal to 1.154700538 and -1.154700538.Subproblem 1
p + 2 = 1.154700538 Simplifying p + 2 = 1.154700538 Reorder the terms: 2 + p = 1.154700538 Solving 2 + p = 1.154700538 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = 1.154700538 + -2 Combine like terms: 2 + -2 = 0 0 + p = 1.154700538 + -2 p = 1.154700538 + -2 Combine like terms: 1.154700538 + -2 = -0.845299462 p = -0.845299462 Simplifying p = -0.845299462Subproblem 2
p + 2 = -1.154700538 Simplifying p + 2 = -1.154700538 Reorder the terms: 2 + p = -1.154700538 Solving 2 + p = -1.154700538 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = -1.154700538 + -2 Combine like terms: 2 + -2 = 0 0 + p = -1.154700538 + -2 p = -1.154700538 + -2 Combine like terms: -1.154700538 + -2 = -3.154700538 p = -3.154700538 Simplifying p = -3.154700538Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.845299462, -3.154700538}Solution
p = {-0.845299462, -3.154700538}
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