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Simplifying x2 + -4.07x + 2.71 = 0 Reorder the terms: 2.71 + -4.07x + x2 = 0 Solving 2.71 + -4.07x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2.71' to each side of the equation. 2.71 + -4.07x + -2.71 + x2 = 0 + -2.71 Reorder the terms: 2.71 + -2.71 + -4.07x + x2 = 0 + -2.71 Combine like terms: 2.71 + -2.71 = 0.00 0.00 + -4.07x + x2 = 0 + -2.71 -4.07x + x2 = 0 + -2.71 Combine like terms: 0 + -2.71 = -2.71 -4.07x + x2 = -2.71 The x term is -4.07x. Take half its coefficient (-2.035). Square it (4.141225) and add it to both sides. Add '4.141225' to each side of the equation. -4.07x + 4.141225 + x2 = -2.71 + 4.141225 Reorder the terms: 4.141225 + -4.07x + x2 = -2.71 + 4.141225 Combine like terms: -2.71 + 4.141225 = 1.431225 4.141225 + -4.07x + x2 = 1.431225 Factor a perfect square on the left side: (x + -2.035)(x + -2.035) = 1.431225 Calculate the square root of the right side: 1.196338163 Break this problem into two subproblems by setting (x + -2.035) equal to 1.196338163 and -1.196338163.Subproblem 1
x + -2.035 = 1.196338163 Simplifying x + -2.035 = 1.196338163 Reorder the terms: -2.035 + x = 1.196338163 Solving -2.035 + x = 1.196338163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.035' to each side of the equation. -2.035 + 2.035 + x = 1.196338163 + 2.035 Combine like terms: -2.035 + 2.035 = 0.000 0.000 + x = 1.196338163 + 2.035 x = 1.196338163 + 2.035 Combine like terms: 1.196338163 + 2.035 = 3.231338163 x = 3.231338163 Simplifying x = 3.231338163Subproblem 2
x + -2.035 = -1.196338163 Simplifying x + -2.035 = -1.196338163 Reorder the terms: -2.035 + x = -1.196338163 Solving -2.035 + x = -1.196338163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.035' to each side of the equation. -2.035 + 2.035 + x = -1.196338163 + 2.035 Combine like terms: -2.035 + 2.035 = 0.000 0.000 + x = -1.196338163 + 2.035 x = -1.196338163 + 2.035 Combine like terms: -1.196338163 + 2.035 = 0.838661837 x = 0.838661837 Simplifying x = 0.838661837Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.231338163, 0.838661837}
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