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Simplifying 3.74x2 + -11.45x + 4.15 = 0 Reorder the terms: 4.15 + -11.45x + 3.74x2 = 0 Solving 4.15 + -11.45x + 3.74x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.74 the coefficient of the squared term: Divide each side by '3.74'. 1.109625668 + -3.061497326x + x2 = 0 Move the constant term to the right: Add '-1.109625668' to each side of the equation. 1.109625668 + -3.061497326x + -1.109625668 + x2 = 0 + -1.109625668 Reorder the terms: 1.109625668 + -1.109625668 + -3.061497326x + x2 = 0 + -1.109625668 Combine like terms: 1.109625668 + -1.109625668 = 0.000000000 0.000000000 + -3.061497326x + x2 = 0 + -1.109625668 -3.061497326x + x2 = 0 + -1.109625668 Combine like terms: 0 + -1.109625668 = -1.109625668 -3.061497326x + x2 = -1.109625668 The x term is -3.061497326x. Take half its coefficient (-1.530748663). Square it (2.343191469) and add it to both sides. Add '2.343191469' to each side of the equation. -3.061497326x + 2.343191469 + x2 = -1.109625668 + 2.343191469 Reorder the terms: 2.343191469 + -3.061497326x + x2 = -1.109625668 + 2.343191469 Combine like terms: -1.109625668 + 2.343191469 = 1.233565801 2.343191469 + -3.061497326x + x2 = 1.233565801 Factor a perfect square on the left side: (x + -1.530748663)(x + -1.530748663) = 1.233565801 Calculate the square root of the right side: 1.110660074 Break this problem into two subproblems by setting (x + -1.530748663) equal to 1.110660074 and -1.110660074.Subproblem 1
x + -1.530748663 = 1.110660074 Simplifying x + -1.530748663 = 1.110660074 Reorder the terms: -1.530748663 + x = 1.110660074 Solving -1.530748663 + x = 1.110660074 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.530748663' to each side of the equation. -1.530748663 + 1.530748663 + x = 1.110660074 + 1.530748663 Combine like terms: -1.530748663 + 1.530748663 = 0.000000000 0.000000000 + x = 1.110660074 + 1.530748663 x = 1.110660074 + 1.530748663 Combine like terms: 1.110660074 + 1.530748663 = 2.641408737 x = 2.641408737 Simplifying x = 2.641408737Subproblem 2
x + -1.530748663 = -1.110660074 Simplifying x + -1.530748663 = -1.110660074 Reorder the terms: -1.530748663 + x = -1.110660074 Solving -1.530748663 + x = -1.110660074 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.530748663' to each side of the equation. -1.530748663 + 1.530748663 + x = -1.110660074 + 1.530748663 Combine like terms: -1.530748663 + 1.530748663 = 0.000000000 0.000000000 + x = -1.110660074 + 1.530748663 x = -1.110660074 + 1.530748663 Combine like terms: -1.110660074 + 1.530748663 = 0.420088589 x = 0.420088589 Simplifying x = 0.420088589Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.641408737, 0.420088589}
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