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Simplifying -1.33x + 0.44 = -1x2 Reorder the terms: 0.44 + -1.33x = -1x2 Solving 0.44 + -1.33x = -1x2 Solving for variable 'x'. Combine like terms: -1x2 + x2 = 0 0.44 + -1.33x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-0.44' to each side of the equation. 0.44 + -1.33x + -0.44 + x2 = 0 + -0.44 Reorder the terms: 0.44 + -0.44 + -1.33x + x2 = 0 + -0.44 Combine like terms: 0.44 + -0.44 = 0.00 0.00 + -1.33x + x2 = 0 + -0.44 -1.33x + x2 = 0 + -0.44 Combine like terms: 0 + -0.44 = -0.44 -1.33x + x2 = -0.44 The x term is -1.33x. Take half its coefficient (-0.665). Square it (0.442225) and add it to both sides. Add '0.442225' to each side of the equation. -1.33x + 0.442225 + x2 = -0.44 + 0.442225 Reorder the terms: 0.442225 + -1.33x + x2 = -0.44 + 0.442225 Combine like terms: -0.44 + 0.442225 = 0.002225 0.442225 + -1.33x + x2 = 0.002225 Factor a perfect square on the left side: (x + -0.665)(x + -0.665) = 0.002225 Calculate the square root of the right side: 0.047169906 Break this problem into two subproblems by setting (x + -0.665) equal to 0.047169906 and -0.047169906.Subproblem 1
x + -0.665 = 0.047169906 Simplifying x + -0.665 = 0.047169906 Reorder the terms: -0.665 + x = 0.047169906 Solving -0.665 + x = 0.047169906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.665' to each side of the equation. -0.665 + 0.665 + x = 0.047169906 + 0.665 Combine like terms: -0.665 + 0.665 = 0.000 0.000 + x = 0.047169906 + 0.665 x = 0.047169906 + 0.665 Combine like terms: 0.047169906 + 0.665 = 0.712169906 x = 0.712169906 Simplifying x = 0.712169906Subproblem 2
x + -0.665 = -0.047169906 Simplifying x + -0.665 = -0.047169906 Reorder the terms: -0.665 + x = -0.047169906 Solving -0.665 + x = -0.047169906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.665' to each side of the equation. -0.665 + 0.665 + x = -0.047169906 + 0.665 Combine like terms: -0.665 + 0.665 = 0.000 0.000 + x = -0.047169906 + 0.665 x = -0.047169906 + 0.665 Combine like terms: -0.047169906 + 0.665 = 0.617830094 x = 0.617830094 Simplifying x = 0.617830094Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.712169906, 0.617830094}
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