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Simplifying 2p2 + -18p + 15 = 0 Reorder the terms: 15 + -18p + 2p2 = 0 Solving 15 + -18p + 2p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + -9p + p2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -9p + -7.5 + p2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -9p + p2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -9p + p2 = 0 + -7.5 -9p + p2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -9p + p2 = -7.5 The p term is -9p. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9p + 20.25 + p2 = -7.5 + 20.25 Reorder the terms: 20.25 + -9p + p2 = -7.5 + 20.25 Combine like terms: -7.5 + 20.25 = 12.75 20.25 + -9p + p2 = 12.75 Factor a perfect square on the left side: (p + -4.5)(p + -4.5) = 12.75 Calculate the square root of the right side: 3.570714214 Break this problem into two subproblems by setting (p + -4.5) equal to 3.570714214 and -3.570714214.Subproblem 1
p + -4.5 = 3.570714214 Simplifying p + -4.5 = 3.570714214 Reorder the terms: -4.5 + p = 3.570714214 Solving -4.5 + p = 3.570714214 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + p = 3.570714214 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = 3.570714214 + 4.5 p = 3.570714214 + 4.5 Combine like terms: 3.570714214 + 4.5 = 8.070714214 p = 8.070714214 Simplifying p = 8.070714214Subproblem 2
p + -4.5 = -3.570714214 Simplifying p + -4.5 = -3.570714214 Reorder the terms: -4.5 + p = -3.570714214 Solving -4.5 + p = -3.570714214 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + p = -3.570714214 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = -3.570714214 + 4.5 p = -3.570714214 + 4.5 Combine like terms: -3.570714214 + 4.5 = 0.929285786 p = 0.929285786 Simplifying p = 0.929285786Solution
The solution to the problem is based on the solutions from the subproblems. p = {8.070714214, 0.929285786}
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