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Simplifying -180 = 64.952p + -4.9p2 Solving -180 = 64.952p + -4.9p2 Solving for variable 'p'. Reorder the terms: -180 + -64.952p + 4.9p2 = 64.952p + -64.952p + -4.9p2 + 4.9p2 Combine like terms: 64.952p + -64.952p = 0.000 -180 + -64.952p + 4.9p2 = 0.000 + -4.9p2 + 4.9p2 -180 + -64.952p + 4.9p2 = -4.9p2 + 4.9p2 Combine like terms: -4.9p2 + 4.9p2 = 0.0 -180 + -64.952p + 4.9p2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -36.73469388 + -13.2555102p + p2 = 0 Move the constant term to the right: Add '36.73469388' to each side of the equation. -36.73469388 + -13.2555102p + 36.73469388 + p2 = 0 + 36.73469388 Reorder the terms: -36.73469388 + 36.73469388 + -13.2555102p + p2 = 0 + 36.73469388 Combine like terms: -36.73469388 + 36.73469388 = 0.00000000 0.00000000 + -13.2555102p + p2 = 0 + 36.73469388 -13.2555102p + p2 = 0 + 36.73469388 Combine like terms: 0 + 36.73469388 = 36.73469388 -13.2555102p + p2 = 36.73469388 The p term is -13.2555102p. Take half its coefficient (-6.6277551). Square it (43.92713767) and add it to both sides. Add '43.92713767' to each side of the equation. -13.2555102p + 43.92713767 + p2 = 36.73469388 + 43.92713767 Reorder the terms: 43.92713767 + -13.2555102p + p2 = 36.73469388 + 43.92713767 Combine like terms: 36.73469388 + 43.92713767 = 80.66183155 43.92713767 + -13.2555102p + p2 = 80.66183155 Factor a perfect square on the left side: (p + -6.6277551)(p + -6.6277551) = 80.66183155 Calculate the square root of the right side: 8.981193214 Break this problem into two subproblems by setting (p + -6.6277551) equal to 8.981193214 and -8.981193214.Subproblem 1
p + -6.6277551 = 8.981193214 Simplifying p + -6.6277551 = 8.981193214 Reorder the terms: -6.6277551 + p = 8.981193214 Solving -6.6277551 + p = 8.981193214 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '6.6277551' to each side of the equation. -6.6277551 + 6.6277551 + p = 8.981193214 + 6.6277551 Combine like terms: -6.6277551 + 6.6277551 = 0.0000000 0.0000000 + p = 8.981193214 + 6.6277551 p = 8.981193214 + 6.6277551 Combine like terms: 8.981193214 + 6.6277551 = 15.608948314 p = 15.608948314 Simplifying p = 15.608948314Subproblem 2
p + -6.6277551 = -8.981193214 Simplifying p + -6.6277551 = -8.981193214 Reorder the terms: -6.6277551 + p = -8.981193214 Solving -6.6277551 + p = -8.981193214 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '6.6277551' to each side of the equation. -6.6277551 + 6.6277551 + p = -8.981193214 + 6.6277551 Combine like terms: -6.6277551 + 6.6277551 = 0.0000000 0.0000000 + p = -8.981193214 + 6.6277551 p = -8.981193214 + 6.6277551 Combine like terms: -8.981193214 + 6.6277551 = -2.353438114 p = -2.353438114 Simplifying p = -2.353438114Solution
The solution to the problem is based on the solutions from the subproblems. p = {15.608948314, -2.353438114}
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