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Simplifying 80.436 = -0.014x2 + 1.253x + 60.976 Reorder the terms: 80.436 = 60.976 + 1.253x + -0.014x2 Solving 80.436 = 60.976 + 1.253x + -0.014x2 Solving for variable 'x'. Combine like terms: 80.436 + -60.976 = 19.46 19.46 + -1.253x + 0.014x2 = 60.976 + 1.253x + -0.014x2 + -60.976 + -1.253x + 0.014x2 Reorder the terms: 19.46 + -1.253x + 0.014x2 = 60.976 + -60.976 + 1.253x + -1.253x + -0.014x2 + 0.014x2 Combine like terms: 60.976 + -60.976 = 0.000 19.46 + -1.253x + 0.014x2 = 0.000 + 1.253x + -1.253x + -0.014x2 + 0.014x2 19.46 + -1.253x + 0.014x2 = 1.253x + -1.253x + -0.014x2 + 0.014x2 Combine like terms: 1.253x + -1.253x = 0.000 19.46 + -1.253x + 0.014x2 = 0.000 + -0.014x2 + 0.014x2 19.46 + -1.253x + 0.014x2 = -0.014x2 + 0.014x2 Combine like terms: -0.014x2 + 0.014x2 = 0.000 19.46 + -1.253x + 0.014x2 = 0.000 Begin completing the square. Divide all terms by 0.014 the coefficient of the squared term: Divide each side by '0.014'. 1390 + -89.5x + x2 = 0 Move the constant term to the right: Add '-1390' to each side of the equation. 1390 + -89.5x + -1390 + x2 = 0 + -1390 Reorder the terms: 1390 + -1390 + -89.5x + x2 = 0 + -1390 Combine like terms: 1390 + -1390 = 0 0 + -89.5x + x2 = 0 + -1390 -89.5x + x2 = 0 + -1390 Combine like terms: 0 + -1390 = -1390 -89.5x + x2 = -1390 The x term is -89.5x. Take half its coefficient (-44.75). Square it (2002.5625) and add it to both sides. Add '2002.5625' to each side of the equation. -89.5x + 2002.5625 + x2 = -1390 + 2002.5625 Reorder the terms: 2002.5625 + -89.5x + x2 = -1390 + 2002.5625 Combine like terms: -1390 + 2002.5625 = 612.5625 2002.5625 + -89.5x + x2 = 612.5625 Factor a perfect square on the left side: (x + -44.75)(x + -44.75) = 612.5625 Calculate the square root of the right side: 24.75 Break this problem into two subproblems by setting (x + -44.75) equal to 24.75 and -24.75.Subproblem 1
x + -44.75 = 24.75 Simplifying x + -44.75 = 24.75 Reorder the terms: -44.75 + x = 24.75 Solving -44.75 + x = 24.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '44.75' to each side of the equation. -44.75 + 44.75 + x = 24.75 + 44.75 Combine like terms: -44.75 + 44.75 = 0.00 0.00 + x = 24.75 + 44.75 x = 24.75 + 44.75 Combine like terms: 24.75 + 44.75 = 69.5 x = 69.5 Simplifying x = 69.5Subproblem 2
x + -44.75 = -24.75 Simplifying x + -44.75 = -24.75 Reorder the terms: -44.75 + x = -24.75 Solving -44.75 + x = -24.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '44.75' to each side of the equation. -44.75 + 44.75 + x = -24.75 + 44.75 Combine like terms: -44.75 + 44.75 = 0.00 0.00 + x = -24.75 + 44.75 x = -24.75 + 44.75 Combine like terms: -24.75 + 44.75 = 20 x = 20 Simplifying x = 20Solution
The solution to the problem is based on the solutions from the subproblems. x = {69.5, 20}
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