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Simplifying -3p2 + -30p + 4 = 0 Reorder the terms: 4 + -30p + -3p2 = 0 Solving 4 + -30p + -3p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1.333333333 + 10p + p2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 10p + 1.333333333 + p2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 10p + p2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 10p + p2 = 0 + 1.333333333 10p + p2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 10p + p2 = 1.333333333 The p term is 10p. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10p + 25 + p2 = 1.333333333 + 25 Reorder the terms: 25 + 10p + p2 = 1.333333333 + 25 Combine like terms: 1.333333333 + 25 = 26.333333333 25 + 10p + p2 = 26.333333333 Factor a perfect square on the left side: (p + 5)(p + 5) = 26.333333333 Calculate the square root of the right side: 5.131601439 Break this problem into two subproblems by setting (p + 5) equal to 5.131601439 and -5.131601439.Subproblem 1
p + 5 = 5.131601439 Simplifying p + 5 = 5.131601439 Reorder the terms: 5 + p = 5.131601439 Solving 5 + p = 5.131601439 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + p = 5.131601439 + -5 Combine like terms: 5 + -5 = 0 0 + p = 5.131601439 + -5 p = 5.131601439 + -5 Combine like terms: 5.131601439 + -5 = 0.131601439 p = 0.131601439 Simplifying p = 0.131601439Subproblem 2
p + 5 = -5.131601439 Simplifying p + 5 = -5.131601439 Reorder the terms: 5 + p = -5.131601439 Solving 5 + p = -5.131601439 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + p = -5.131601439 + -5 Combine like terms: 5 + -5 = 0 0 + p = -5.131601439 + -5 p = -5.131601439 + -5 Combine like terms: -5.131601439 + -5 = -10.131601439 p = -10.131601439 Simplifying p = -10.131601439Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.131601439, -10.131601439}
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