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Simplifying 3p2 + 18p = -23 Reorder the terms: 18p + 3p2 = -23 Solving 18p + 3p2 = -23 Solving for variable 'p'. Reorder the terms: 23 + 18p + 3p2 = -23 + 23 Combine like terms: -23 + 23 = 0 23 + 18p + 3p2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 7.666666667 + 6p + p2 = 0 Move the constant term to the right: Add '-7.666666667' to each side of the equation. 7.666666667 + 6p + -7.666666667 + p2 = 0 + -7.666666667 Reorder the terms: 7.666666667 + -7.666666667 + 6p + p2 = 0 + -7.666666667 Combine like terms: 7.666666667 + -7.666666667 = 0.000000000 0.000000000 + 6p + p2 = 0 + -7.666666667 6p + p2 = 0 + -7.666666667 Combine like terms: 0 + -7.666666667 = -7.666666667 6p + p2 = -7.666666667 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 = -7.666666667 + 9 Reorder the terms: 9 + 6p + p2 = -7.666666667 + 9 Combine like terms: -7.666666667 + 9 = 1.333333333 9 + 6p + p2 = 1.333333333 Factor a perfect square on the left side: (p + 3)(p + 3) = 1.333333333 Calculate the square root of the right side: 1.154700538 Break this problem into two subproblems by setting (p + 3) equal to 1.154700538 and -1.154700538.Subproblem 1
p + 3 = 1.154700538 Simplifying p + 3 = 1.154700538 Reorder the terms: 3 + p = 1.154700538 Solving 3 + p = 1.154700538 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 = 1.154700538 + -3 Combine like terms: 3 + -3 = 0 0 + p = 1.154700538 + -3 p = 1.154700538 + -3 Combine like terms: 1.154700538 + -3 = -1.845299462 p = -1.845299462 Simplifying p = -1.845299462Subproblem 2
p + 3 = -1.154700538 Simplifying p + 3 = -1.154700538 Reorder the terms: 3 + p = -1.154700538 Solving 3 + p = -1.154700538 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 = -1.154700538 + -3 Combine like terms: 3 + -3 = 0 0 + p = -1.154700538 + -3 p = -1.154700538 + -3 Combine like terms: -1.154700538 + -3 = -4.154700538 p = -4.154700538 Simplifying p = -4.154700538Solution
The solution to the problem is based on the solutions from the subproblems. p = {-1.845299462, -4.154700538}
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