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Simplifying 3p2 = 8 + -15p Solving 3p2 = 8 + -15p Solving for variable 'p'. Reorder the terms: -8 + 15p + 3p2 = 8 + -15p + -8 + 15p Reorder the terms: -8 + 15p + 3p2 = 8 + -8 + -15p + 15p Combine like terms: 8 + -8 = 0 -8 + 15p + 3p2 = 0 + -15p + 15p -8 + 15p + 3p2 = -15p + 15p Combine like terms: -15p + 15p = 0 -8 + 15p + 3p2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.666666667 + 5p + p2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + 5p + 2.666666667 + p2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + 5p + p2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + 5p + p2 = 0 + 2.666666667 5p + p2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 5p + p2 = 2.666666667 The p term is 5p. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5p + 6.25 + p2 = 2.666666667 + 6.25 Reorder the terms: 6.25 + 5p + p2 = 2.666666667 + 6.25 Combine like terms: 2.666666667 + 6.25 = 8.916666667 6.25 + 5p + p2 = 8.916666667 Factor a perfect square on the left side: (p + 2.5)(p + 2.5) = 8.916666667 Calculate the square root of the right side: 2.986078811 Break this problem into two subproblems by setting (p + 2.5) equal to 2.986078811 and -2.986078811.Subproblem 1
p + 2.5 = 2.986078811 Simplifying p + 2.5 = 2.986078811 Reorder the terms: 2.5 + p = 2.986078811 Solving 2.5 + p = 2.986078811 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + p = 2.986078811 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + p = 2.986078811 + -2.5 p = 2.986078811 + -2.5 Combine like terms: 2.986078811 + -2.5 = 0.486078811 p = 0.486078811 Simplifying p = 0.486078811Subproblem 2
p + 2.5 = -2.986078811 Simplifying p + 2.5 = -2.986078811 Reorder the terms: 2.5 + p = -2.986078811 Solving 2.5 + p = -2.986078811 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + p = -2.986078811 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + p = -2.986078811 + -2.5 p = -2.986078811 + -2.5 Combine like terms: -2.986078811 + -2.5 = -5.486078811 p = -5.486078811 Simplifying p = -5.486078811Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.486078811, -5.486078811}
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