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Simplifying -3p2 + 84p + 33 = 0 Reorder the terms: 33 + 84p + -3p2 = 0 Solving 33 + 84p + -3p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '3'. 3(11 + 28p + -1p2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(11 + 28p + -1p2)' equal to zero and attempt to solve: Simplifying 11 + 28p + -1p2 = 0 Solving 11 + 28p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -11 + -28p + p2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -28p + 11 + p2 = 0 + 11 Reorder the terms: -11 + 11 + -28p + p2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -28p + p2 = 0 + 11 -28p + p2 = 0 + 11 Combine like terms: 0 + 11 = 11 -28p + p2 = 11 The p term is -28p. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28p + 196 + p2 = 11 + 196 Reorder the terms: 196 + -28p + p2 = 11 + 196 Combine like terms: 11 + 196 = 207 196 + -28p + p2 = 207 Factor a perfect square on the left side: (p + -14)(p + -14) = 207 Calculate the square root of the right side: 14.38749457 Break this problem into two subproblems by setting (p + -14) equal to 14.38749457 and -14.38749457.Subproblem 1
p + -14 = 14.38749457 Simplifying p + -14 = 14.38749457 Reorder the terms: -14 + p = 14.38749457 Solving -14 + p = 14.38749457 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + p = 14.38749457 + 14 Combine like terms: -14 + 14 = 0 0 + p = 14.38749457 + 14 p = 14.38749457 + 14 Combine like terms: 14.38749457 + 14 = 28.38749457 p = 28.38749457 Simplifying p = 28.38749457Subproblem 2
p + -14 = -14.38749457 Simplifying p + -14 = -14.38749457 Reorder the terms: -14 + p = -14.38749457 Solving -14 + p = -14.38749457 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + p = -14.38749457 + 14 Combine like terms: -14 + 14 = 0 0 + p = -14.38749457 + 14 p = -14.38749457 + 14 Combine like terms: -14.38749457 + 14 = -0.38749457 p = -0.38749457 Simplifying p = -0.38749457Solution
The solution to the problem is based on the solutions from the subproblems. p = {28.38749457, -0.38749457}Solution
p = {28.38749457, -0.38749457}
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