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Simplifying 3.61 + x(0.035 + x) = 5 3.61 + (0.035 * x + x * x) = 5 3.61 + (0.035x + x2) = 5 Solving 3.61 + 0.035x + x2 = 5 Solving for variable 'x'. Reorder the terms: 3.61 + -5 + 0.035x + x2 = 5 + -5 Combine like terms: 3.61 + -5 = -1.39 -1.39 + 0.035x + x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -1.39 + 0.035x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1.39' to each side of the equation. -1.39 + 0.035x + 1.39 + x2 = 0 + 1.39 Reorder the terms: -1.39 + 1.39 + 0.035x + x2 = 0 + 1.39 Combine like terms: -1.39 + 1.39 = 0.00 0.00 + 0.035x + x2 = 0 + 1.39 0.035x + x2 = 0 + 1.39 Combine like terms: 0 + 1.39 = 1.39 0.035x + x2 = 1.39 The x term is 0.035x. Take half its coefficient (0.0175). Square it (0.00030625) and add it to both sides. Add '0.00030625' to each side of the equation. 0.035x + 0.00030625 + x2 = 1.39 + 0.00030625 Reorder the terms: 0.00030625 + 0.035x + x2 = 1.39 + 0.00030625 Combine like terms: 1.39 + 0.00030625 = 1.39030625 0.00030625 + 0.035x + x2 = 1.39030625 Factor a perfect square on the left side: (x + 0.0175)(x + 0.0175) = 1.39030625 Calculate the square root of the right side: 1.179112484 Break this problem into two subproblems by setting (x + 0.0175) equal to 1.179112484 and -1.179112484.Subproblem 1
x + 0.0175 = 1.179112484 Simplifying x + 0.0175 = 1.179112484 Reorder the terms: 0.0175 + x = 1.179112484 Solving 0.0175 + x = 1.179112484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0175' to each side of the equation. 0.0175 + -0.0175 + x = 1.179112484 + -0.0175 Combine like terms: 0.0175 + -0.0175 = 0.0000 0.0000 + x = 1.179112484 + -0.0175 x = 1.179112484 + -0.0175 Combine like terms: 1.179112484 + -0.0175 = 1.161612484 x = 1.161612484 Simplifying x = 1.161612484Subproblem 2
x + 0.0175 = -1.179112484 Simplifying x + 0.0175 = -1.179112484 Reorder the terms: 0.0175 + x = -1.179112484 Solving 0.0175 + x = -1.179112484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0175' to each side of the equation. 0.0175 + -0.0175 + x = -1.179112484 + -0.0175 Combine like terms: 0.0175 + -0.0175 = 0.0000 0.0000 + x = -1.179112484 + -0.0175 x = -1.179112484 + -0.0175 Combine like terms: -1.179112484 + -0.0175 = -1.196612484 x = -1.196612484 Simplifying x = -1.196612484Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.161612484, -1.196612484}
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