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Simplifying 3p2 + 18p + -11 = 0 Reorder the terms: -11 + 18p + 3p2 = 0 Solving -11 + 18p + 3p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.666666667 + 6p + p2 = 0 Move the constant term to the right: Add '3.666666667' to each side of the equation. -3.666666667 + 6p + 3.666666667 + p2 = 0 + 3.666666667 Reorder the terms: -3.666666667 + 3.666666667 + 6p + p2 = 0 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + 6p + p2 = 0 + 3.666666667 6p + p2 = 0 + 3.666666667 Combine like terms: 0 + 3.666666667 = 3.666666667 6p + p2 = 3.666666667 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 = 3.666666667 + 9 Reorder the terms: 9 + 6p + p2 = 3.666666667 + 9 Combine like terms: 3.666666667 + 9 = 12.666666667 9 + 6p + p2 = 12.666666667 Factor a perfect square on the left side: (p + 3)(p + 3) = 12.666666667 Calculate the square root of the right side: 3.559026084 Break this problem into two subproblems by setting (p + 3) equal to 3.559026084 and -3.559026084.Subproblem 1
p + 3 = 3.559026084 Simplifying p + 3 = 3.559026084 Reorder the terms: 3 + p = 3.559026084 Solving 3 + p = 3.559026084 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 = 3.559026084 + -3 Combine like terms: 3 + -3 = 0 0 + p = 3.559026084 + -3 p = 3.559026084 + -3 Combine like terms: 3.559026084 + -3 = 0.559026084 p = 0.559026084 Simplifying p = 0.559026084Subproblem 2
p + 3 = -3.559026084 Simplifying p + 3 = -3.559026084 Reorder the terms: 3 + p = -3.559026084 Solving 3 + p = -3.559026084 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 = -3.559026084 + -3 Combine like terms: 3 + -3 = 0 0 + p = -3.559026084 + -3 p = -3.559026084 + -3 Combine like terms: -3.559026084 + -3 = -6.559026084 p = -6.559026084 Simplifying p = -6.559026084Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.559026084, -6.559026084}
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