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Simplifying 10p2 + 9p + -94 = 0 Reorder the terms: -94 + 9p + 10p2 = 0 Solving -94 + 9p + 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'. -9.4 + 0.9p + p2 = 0 Move the constant term to the right: Add '9.4' to each side of the equation. -9.4 + 0.9p + 9.4 + p2 = 0 + 9.4 Reorder the terms: -9.4 + 9.4 + 0.9p + p2 = 0 + 9.4 Combine like terms: -9.4 + 9.4 = 0.0 0.0 + 0.9p + p2 = 0 + 9.4 0.9p + p2 = 0 + 9.4 Combine like terms: 0 + 9.4 = 9.4 0.9p + p2 = 9.4 The p term is 0.9p. Take half its coefficient (0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. 0.9p + 0.2025 + p2 = 9.4 + 0.2025 Reorder the terms: 0.2025 + 0.9p + p2 = 9.4 + 0.2025 Combine like terms: 9.4 + 0.2025 = 9.6025 0.2025 + 0.9p + p2 = 9.6025 Factor a perfect square on the left side: (p + 0.45)(p + 0.45) = 9.6025 Calculate the square root of the right side: 3.098790086 Break this problem into two subproblems by setting (p + 0.45) equal to 3.098790086 and -3.098790086.Subproblem 1
p + 0.45 = 3.098790086 Simplifying p + 0.45 = 3.098790086 Reorder the terms: 0.45 + p = 3.098790086 Solving 0.45 + p = 3.098790086 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + p = 3.098790086 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + p = 3.098790086 + -0.45 p = 3.098790086 + -0.45 Combine like terms: 3.098790086 + -0.45 = 2.648790086 p = 2.648790086 Simplifying p = 2.648790086Subproblem 2
p + 0.45 = -3.098790086 Simplifying p + 0.45 = -3.098790086 Reorder the terms: 0.45 + p = -3.098790086 Solving 0.45 + p = -3.098790086 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + p = -3.098790086 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + p = -3.098790086 + -0.45 p = -3.098790086 + -0.45 Combine like terms: -3.098790086 + -0.45 = -3.548790086 p = -3.548790086 Simplifying p = -3.548790086Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.648790086, -3.548790086}
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