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Simplifying 4p2 + -18p + -84 = 0 Reorder the terms: -84 + -18p + 4p2 = 0 Solving -84 + -18p + 4p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(-42 + -9p + 2p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-42 + -9p + 2p2)' equal to zero and attempt to solve: Simplifying -42 + -9p + 2p2 = 0 Solving -42 + -9p + 2p2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -21 + -4.5p + p2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + -4.5p + 21 + p2 = 0 + 21 Reorder the terms: -21 + 21 + -4.5p + p2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -4.5p + p2 = 0 + 21 -4.5p + p2 = 0 + 21 Combine like terms: 0 + 21 = 21 -4.5p + p2 = 21 The p term is -4.5p. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5p + 5.0625 + p2 = 21 + 5.0625 Reorder the terms: 5.0625 + -4.5p + p2 = 21 + 5.0625 Combine like terms: 21 + 5.0625 = 26.0625 5.0625 + -4.5p + p2 = 26.0625 Factor a perfect square on the left side: (p + -2.25)(p + -2.25) = 26.0625 Calculate the square root of the right side: 5.105144464 Break this problem into two subproblems by setting (p + -2.25) equal to 5.105144464 and -5.105144464.Subproblem 1
p + -2.25 = 5.105144464 Simplifying p + -2.25 = 5.105144464 Reorder the terms: -2.25 + p = 5.105144464 Solving -2.25 + p = 5.105144464 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + p = 5.105144464 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + p = 5.105144464 + 2.25 p = 5.105144464 + 2.25 Combine like terms: 5.105144464 + 2.25 = 7.355144464 p = 7.355144464 Simplifying p = 7.355144464Subproblem 2
p + -2.25 = -5.105144464 Simplifying p + -2.25 = -5.105144464 Reorder the terms: -2.25 + p = -5.105144464 Solving -2.25 + p = -5.105144464 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + p = -5.105144464 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + p = -5.105144464 + 2.25 p = -5.105144464 + 2.25 Combine like terms: -5.105144464 + 2.25 = -2.855144464 p = -2.855144464 Simplifying p = -2.855144464Solution
The solution to the problem is based on the solutions from the subproblems. p = {7.355144464, -2.855144464}Solution
p = {7.355144464, -2.855144464}
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