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Simplifying 15(10p + -7) * 13p = 58 Reorder the terms: 15(-7 + 10p) * 13p = 58 Reorder the terms for easier multiplication: 15 * 13p(-7 + 10p) = 58 Multiply 15 * 13 195p(-7 + 10p) = 58 (-7 * 195p + 10p * 195p) = 58 (-1365p + 1950p2) = 58 Solving -1365p + 1950p2 = 58 Solving for variable 'p'. Reorder the terms: -58 + -1365p + 1950p2 = 58 + -58 Combine like terms: 58 + -58 = 0 -58 + -1365p + 1950p2 = 0 Begin completing the square. Divide all terms by 1950 the coefficient of the squared term: Divide each side by '1950'. -0.02974358974 + -0.7p + p2 = 0.0 Move the constant term to the right: Add '0.02974358974' to each side of the equation. -0.02974358974 + -0.7p + 0.02974358974 + p2 = 0.0 + 0.02974358974 Reorder the terms: -0.02974358974 + 0.02974358974 + -0.7p + p2 = 0.0 + 0.02974358974 Combine like terms: -0.02974358974 + 0.02974358974 = 0.00000000000 0.00000000000 + -0.7p + p2 = 0.0 + 0.02974358974 -0.7p + p2 = 0.0 + 0.02974358974 Combine like terms: 0.0 + 0.02974358974 = 0.02974358974 -0.7p + p2 = 0.02974358974 The p term is -0.7p. Take half its coefficient (-0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. -0.7p + 0.1225 + p2 = 0.02974358974 + 0.1225 Reorder the terms: 0.1225 + -0.7p + p2 = 0.02974358974 + 0.1225 Combine like terms: 0.02974358974 + 0.1225 = 0.15224358974 0.1225 + -0.7p + p2 = 0.15224358974 Factor a perfect square on the left side: (p + -0.35)(p + -0.35) = 0.15224358974 Calculate the square root of the right side: 0.390184046 Break this problem into two subproblems by setting (p + -0.35) equal to 0.390184046 and -0.390184046.Subproblem 1
p + -0.35 = 0.390184046 Simplifying p + -0.35 = 0.390184046 Reorder the terms: -0.35 + p = 0.390184046 Solving -0.35 + p = 0.390184046 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + p = 0.390184046 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + p = 0.390184046 + 0.35 p = 0.390184046 + 0.35 Combine like terms: 0.390184046 + 0.35 = 0.740184046 p = 0.740184046 Simplifying p = 0.740184046Subproblem 2
p + -0.35 = -0.390184046 Simplifying p + -0.35 = -0.390184046 Reorder the terms: -0.35 + p = -0.390184046 Solving -0.35 + p = -0.390184046 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + p = -0.390184046 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + p = -0.390184046 + 0.35 p = -0.390184046 + 0.35 Combine like terms: -0.390184046 + 0.35 = -0.040184046 p = -0.040184046 Simplifying p = -0.040184046Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.740184046, -0.040184046}
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