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Simplifying 10p2 + 31p + -121 = 0 Reorder the terms: -121 + 31p + 10p2 = 0 Solving -121 + 31p + 10p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -12.1 + 3.1p + p2 = 0 Move the constant term to the right: Add '12.1' to each side of the equation. -12.1 + 3.1p + 12.1 + p2 = 0 + 12.1 Reorder the terms: -12.1 + 12.1 + 3.1p + p2 = 0 + 12.1 Combine like terms: -12.1 + 12.1 = 0.0 0.0 + 3.1p + p2 = 0 + 12.1 3.1p + p2 = 0 + 12.1 Combine like terms: 0 + 12.1 = 12.1 3.1p + p2 = 12.1 The p term is 3.1p. Take half its coefficient (1.55). Square it (2.4025) and add it to both sides. Add '2.4025' to each side of the equation. 3.1p + 2.4025 + p2 = 12.1 + 2.4025 Reorder the terms: 2.4025 + 3.1p + p2 = 12.1 + 2.4025 Combine like terms: 12.1 + 2.4025 = 14.5025 2.4025 + 3.1p + p2 = 14.5025 Factor a perfect square on the left side: (p + 1.55)(p + 1.55) = 14.5025 Calculate the square root of the right side: 3.808214805 Break this problem into two subproblems by setting (p + 1.55) equal to 3.808214805 and -3.808214805.Subproblem 1
p + 1.55 = 3.808214805 Simplifying p + 1.55 = 3.808214805 Reorder the terms: 1.55 + p = 3.808214805 Solving 1.55 + p = 3.808214805 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.55' to each side of the equation. 1.55 + -1.55 + p = 3.808214805 + -1.55 Combine like terms: 1.55 + -1.55 = 0.00 0.00 + p = 3.808214805 + -1.55 p = 3.808214805 + -1.55 Combine like terms: 3.808214805 + -1.55 = 2.258214805 p = 2.258214805 Simplifying p = 2.258214805Subproblem 2
p + 1.55 = -3.808214805 Simplifying p + 1.55 = -3.808214805 Reorder the terms: 1.55 + p = -3.808214805 Solving 1.55 + p = -3.808214805 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.55' to each side of the equation. 1.55 + -1.55 + p = -3.808214805 + -1.55 Combine like terms: 1.55 + -1.55 = 0.00 0.00 + p = -3.808214805 + -1.55 p = -3.808214805 + -1.55 Combine like terms: -3.808214805 + -1.55 = -5.358214805 p = -5.358214805 Simplifying p = -5.358214805Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.258214805, -5.358214805}
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