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Simplifying x2 + 0.02044536x + -1(0.0002657894985) = 0 Multiply -1 * 0.0002657894985 x2 + 0.02044536x + -0.0002657894985 = 0 Reorder the terms: -0.0002657894985 + 0.02044536x + x2 = 0 Solving -0.0002657894985 + 0.02044536x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.0002657894985' to each side of the equation. -0.0002657894985 + 0.02044536x + 0.0002657894985 + x2 = 0 + 0.0002657894985 Reorder the terms: -0.0002657894985 + 0.0002657894985 + 0.02044536x + x2 = 0 + 0.0002657894985 Combine like terms: -0.0002657894985 + 0.0002657894985 = 0.0000000000000 0.0000000000000 + 0.02044536x + x2 = 0 + 0.0002657894985 0.02044536x + x2 = 0 + 0.0002657894985 Combine like terms: 0 + 0.0002657894985 = 0.0002657894985 0.02044536x + x2 = 0.0002657894985 The x term is 0.02044536x. Take half its coefficient (0.01022268). Square it (0.0001045031864) and add it to both sides. Add '0.0001045031864' to each side of the equation. 0.02044536x + 0.0001045031864 + x2 = 0.0002657894985 + 0.0001045031864 Reorder the terms: 0.0001045031864 + 0.02044536x + x2 = 0.0002657894985 + 0.0001045031864 Combine like terms: 0.0002657894985 + 0.0001045031864 = 0.0003702926849 0.0001045031864 + 0.02044536x + x2 = 0.0003702926849 Factor a perfect square on the left side: (x + 0.01022268)(x + 0.01022268) = 0.0003702926849 Calculate the square root of the right side: 0.019242991 Break this problem into two subproblems by setting (x + 0.01022268) equal to 0.019242991 and -0.019242991.Subproblem 1
x + 0.01022268 = 0.019242991 Simplifying x + 0.01022268 = 0.019242991 Reorder the terms: 0.01022268 + x = 0.019242991 Solving 0.01022268 + x = 0.019242991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01022268' to each side of the equation. 0.01022268 + -0.01022268 + x = 0.019242991 + -0.01022268 Combine like terms: 0.01022268 + -0.01022268 = 0.00000000 0.00000000 + x = 0.019242991 + -0.01022268 x = 0.019242991 + -0.01022268 Combine like terms: 0.019242991 + -0.01022268 = 0.009020311 x = 0.009020311 Simplifying x = 0.009020311Subproblem 2
x + 0.01022268 = -0.019242991 Simplifying x + 0.01022268 = -0.019242991 Reorder the terms: 0.01022268 + x = -0.019242991 Solving 0.01022268 + x = -0.019242991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01022268' to each side of the equation. 0.01022268 + -0.01022268 + x = -0.019242991 + -0.01022268 Combine like terms: 0.01022268 + -0.01022268 = 0.00000000 0.00000000 + x = -0.019242991 + -0.01022268 x = -0.019242991 + -0.01022268 Combine like terms: -0.019242991 + -0.01022268 = -0.029465671 x = -0.029465671 Simplifying x = -0.029465671Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.009020311, -0.029465671}
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