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Simplifying x2 + -1x + 0.08 = 0 Reorder the terms: 0.08 + -1x + x2 = 0 Solving 0.08 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.08' to each side of the equation. 0.08 + -1x + -0.08 + x2 = 0 + -0.08 Reorder the terms: 0.08 + -0.08 + -1x + x2 = 0 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 0.00 + -1x + x2 = 0 + -0.08 -1x + x2 = 0 + -0.08 Combine like terms: 0 + -0.08 = -0.08 -1x + x2 = -0.08 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -0.08 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.08 + 0.25 Combine like terms: -0.08 + 0.25 = 0.17 0.25 + -1x + x2 = 0.17 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.17 Calculate the square root of the right side: 0.412310563 Break this problem into two subproblems by setting (x + -0.5) equal to 0.412310563 and -0.412310563.Subproblem 1
x + -0.5 = 0.412310563 Simplifying x + -0.5 = 0.412310563 Reorder the terms: -0.5 + x = 0.412310563 Solving -0.5 + x = 0.412310563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.412310563 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.412310563 + 0.5 x = 0.412310563 + 0.5 Combine like terms: 0.412310563 + 0.5 = 0.912310563 x = 0.912310563 Simplifying x = 0.912310563Subproblem 2
x + -0.5 = -0.412310563 Simplifying x + -0.5 = -0.412310563 Reorder the terms: -0.5 + x = -0.412310563 Solving -0.5 + x = -0.412310563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.412310563 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.412310563 + 0.5 x = -0.412310563 + 0.5 Combine like terms: -0.412310563 + 0.5 = 0.087689437 x = 0.087689437 Simplifying x = 0.087689437Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.912310563, 0.087689437}
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