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Simplifying x2 + -0.82x = 0.046 Reorder the terms: -0.82x + x2 = 0.046 Solving -0.82x + x2 = 0.046 Solving for variable 'x'. Reorder the terms: -0.046 + -0.82x + x2 = 0.046 + -0.046 Combine like terms: 0.046 + -0.046 = 0.000 -0.046 + -0.82x + x2 = 0.000 Begin completing the square. Move the constant term to the right: Add '0.046' to each side of the equation. -0.046 + -0.82x + 0.046 + x2 = 0.000 + 0.046 Reorder the terms: -0.046 + 0.046 + -0.82x + x2 = 0.000 + 0.046 Combine like terms: -0.046 + 0.046 = 0.000 0.000 + -0.82x + x2 = 0.000 + 0.046 -0.82x + x2 = 0.000 + 0.046 Combine like terms: 0.000 + 0.046 = 0.046 -0.82x + x2 = 0.046 The x term is -0.82x. Take half its coefficient (-0.41). Square it (0.1681) and add it to both sides. Add '0.1681' to each side of the equation. -0.82x + 0.1681 + x2 = 0.046 + 0.1681 Reorder the terms: 0.1681 + -0.82x + x2 = 0.046 + 0.1681 Combine like terms: 0.046 + 0.1681 = 0.2141 0.1681 + -0.82x + x2 = 0.2141 Factor a perfect square on the left side: (x + -0.41)(x + -0.41) = 0.2141 Calculate the square root of the right side: 0.462709412 Break this problem into two subproblems by setting (x + -0.41) equal to 0.462709412 and -0.462709412.Subproblem 1
x + -0.41 = 0.462709412 Simplifying x + -0.41 = 0.462709412 Reorder the terms: -0.41 + x = 0.462709412 Solving -0.41 + x = 0.462709412 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.41' to each side of the equation. -0.41 + 0.41 + x = 0.462709412 + 0.41 Combine like terms: -0.41 + 0.41 = 0.00 0.00 + x = 0.462709412 + 0.41 x = 0.462709412 + 0.41 Combine like terms: 0.462709412 + 0.41 = 0.872709412 x = 0.872709412 Simplifying x = 0.872709412Subproblem 2
x + -0.41 = -0.462709412 Simplifying x + -0.41 = -0.462709412 Reorder the terms: -0.41 + x = -0.462709412 Solving -0.41 + x = -0.462709412 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.41' to each side of the equation. -0.41 + 0.41 + x = -0.462709412 + 0.41 Combine like terms: -0.41 + 0.41 = 0.00 0.00 + x = -0.462709412 + 0.41 x = -0.462709412 + 0.41 Combine like terms: -0.462709412 + 0.41 = -0.052709412 x = -0.052709412 Simplifying x = -0.052709412Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.872709412, -0.052709412}
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