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Simplifying 24 = 1.76x2 + -13.32x + 41 Reorder the terms: 24 = 41 + -13.32x + 1.76x2 Solving 24 = 41 + -13.32x + 1.76x2 Solving for variable 'x'. Combine like terms: 24 + -41 = -17 -17 + 13.32x + -1.76x2 = 41 + -13.32x + 1.76x2 + -41 + 13.32x + -1.76x2 Reorder the terms: -17 + 13.32x + -1.76x2 = 41 + -41 + -13.32x + 13.32x + 1.76x2 + -1.76x2 Combine like terms: 41 + -41 = 0 -17 + 13.32x + -1.76x2 = 0 + -13.32x + 13.32x + 1.76x2 + -1.76x2 -17 + 13.32x + -1.76x2 = -13.32x + 13.32x + 1.76x2 + -1.76x2 Combine like terms: -13.32x + 13.32x = 0.00 -17 + 13.32x + -1.76x2 = 0.00 + 1.76x2 + -1.76x2 -17 + 13.32x + -1.76x2 = 1.76x2 + -1.76x2 Combine like terms: 1.76x2 + -1.76x2 = 0.00 -17 + 13.32x + -1.76x2 = 0.00 Begin completing the square. Divide all terms by -1.76 the coefficient of the squared term: Divide each side by '-1.76'. 9.659090909 + -7.568181818x + x2 = 0 Move the constant term to the right: Add '-9.659090909' to each side of the equation. 9.659090909 + -7.568181818x + -9.659090909 + x2 = 0 + -9.659090909 Reorder the terms: 9.659090909 + -9.659090909 + -7.568181818x + x2 = 0 + -9.659090909 Combine like terms: 9.659090909 + -9.659090909 = 0.000000000 0.000000000 + -7.568181818x + x2 = 0 + -9.659090909 -7.568181818x + x2 = 0 + -9.659090909 Combine like terms: 0 + -9.659090909 = -9.659090909 -7.568181818x + x2 = -9.659090909 The x term is -7.568181818x. Take half its coefficient (-3.784090909). Square it (14.31934401) and add it to both sides. Add '14.31934401' to each side of the equation. -7.568181818x + 14.31934401 + x2 = -9.659090909 + 14.31934401 Reorder the terms: 14.31934401 + -7.568181818x + x2 = -9.659090909 + 14.31934401 Combine like terms: -9.659090909 + 14.31934401 = 4.660253101 14.31934401 + -7.568181818x + x2 = 4.660253101 Factor a perfect square on the left side: (x + -3.784090909)(x + -3.784090909) = 4.660253101 Calculate the square root of the right side: 2.158761937 Break this problem into two subproblems by setting (x + -3.784090909) equal to 2.158761937 and -2.158761937.Subproblem 1
x + -3.784090909 = 2.158761937 Simplifying x + -3.784090909 = 2.158761937 Reorder the terms: -3.784090909 + x = 2.158761937 Solving -3.784090909 + x = 2.158761937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.784090909' to each side of the equation. -3.784090909 + 3.784090909 + x = 2.158761937 + 3.784090909 Combine like terms: -3.784090909 + 3.784090909 = 0.000000000 0.000000000 + x = 2.158761937 + 3.784090909 x = 2.158761937 + 3.784090909 Combine like terms: 2.158761937 + 3.784090909 = 5.942852846 x = 5.942852846 Simplifying x = 5.942852846Subproblem 2
x + -3.784090909 = -2.158761937 Simplifying x + -3.784090909 = -2.158761937 Reorder the terms: -3.784090909 + x = -2.158761937 Solving -3.784090909 + x = -2.158761937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.784090909' to each side of the equation. -3.784090909 + 3.784090909 + x = -2.158761937 + 3.784090909 Combine like terms: -3.784090909 + 3.784090909 = 0.000000000 0.000000000 + x = -2.158761937 + 3.784090909 x = -2.158761937 + 3.784090909 Combine like terms: -2.158761937 + 3.784090909 = 1.625328972 x = 1.625328972 Simplifying x = 1.625328972Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.942852846, 1.625328972}
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