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Simplifying 3p * 3p + -5p + -28 = 0 Reorder the terms for easier multiplication: 3 * 3p * p + -5p + -28 = 0 Multiply 3 * 3 9p * p + -5p + -28 = 0 Multiply p * p 9p2 + -5p + -28 = 0 Reorder the terms: -28 + -5p + 9p2 = 0 Solving -28 + -5p + 9p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -3.111111111 + -0.5555555556p + p2 = 0 Move the constant term to the right: Add '3.111111111' to each side of the equation. -3.111111111 + -0.5555555556p + 3.111111111 + p2 = 0 + 3.111111111 Reorder the terms: -3.111111111 + 3.111111111 + -0.5555555556p + p2 = 0 + 3.111111111 Combine like terms: -3.111111111 + 3.111111111 = 0.000000000 0.000000000 + -0.5555555556p + p2 = 0 + 3.111111111 -0.5555555556p + p2 = 0 + 3.111111111 Combine like terms: 0 + 3.111111111 = 3.111111111 -0.5555555556p + p2 = 3.111111111 The p term is -0.5555555556p. Take half its coefficient (-0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. -0.5555555556p + 0.07716049384 + p2 = 3.111111111 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556p + p2 = 3.111111111 + 0.07716049384 Combine like terms: 3.111111111 + 0.07716049384 = 3.18827160484 0.07716049384 + -0.5555555556p + p2 = 3.18827160484 Factor a perfect square on the left side: (p + -0.2777777778)(p + -0.2777777778) = 3.18827160484 Calculate the square root of the right side: 1.785573187 Break this problem into two subproblems by setting (p + -0.2777777778) equal to 1.785573187 and -1.785573187.Subproblem 1
p + -0.2777777778 = 1.785573187 Simplifying p + -0.2777777778 = 1.785573187 Reorder the terms: -0.2777777778 + p = 1.785573187 Solving -0.2777777778 + p = 1.785573187 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + p = 1.785573187 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + p = 1.785573187 + 0.2777777778 p = 1.785573187 + 0.2777777778 Combine like terms: 1.785573187 + 0.2777777778 = 2.0633509648 p = 2.0633509648 Simplifying p = 2.0633509648Subproblem 2
p + -0.2777777778 = -1.785573187 Simplifying p + -0.2777777778 = -1.785573187 Reorder the terms: -0.2777777778 + p = -1.785573187 Solving -0.2777777778 + p = -1.785573187 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + p = -1.785573187 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + p = -1.785573187 + 0.2777777778 p = -1.785573187 + 0.2777777778 Combine like terms: -1.785573187 + 0.2777777778 = -1.5077954092 p = -1.5077954092 Simplifying p = -1.5077954092Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.0633509648, -1.5077954092}
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