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Simplifying 2x2 + -2x = 82 Reorder the terms: -2x + 2x2 = 82 Solving -2x + 2x2 = 82 Solving for variable 'x'. Reorder the terms: -82 + -2x + 2x2 = 82 + -82 Combine like terms: 82 + -82 = 0 -82 + -2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-41 + -1x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-41 + -1x + x2)' equal to zero and attempt to solve: Simplifying -41 + -1x + x2 = 0 Solving -41 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + -1x + 41 + x2 = 0 + 41 Reorder the terms: -41 + 41 + -1x + x2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -1x + x2 = 0 + 41 -1x + x2 = 0 + 41 Combine like terms: 0 + 41 = 41 -1x + x2 = 41 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 = 41 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 41 + 0.25 Combine like terms: 41 + 0.25 = 41.25 0.25 + -1x + x2 = 41.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 41.25 Calculate the square root of the right side: 6.422616289 Break this problem into two subproblems by setting (x + -0.5) equal to 6.422616289 and -6.422616289.Subproblem 1
x + -0.5 = 6.422616289 Simplifying x + -0.5 = 6.422616289 Reorder the terms: -0.5 + x = 6.422616289 Solving -0.5 + x = 6.422616289 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 = 6.422616289 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 6.422616289 + 0.5 x = 6.422616289 + 0.5 Combine like terms: 6.422616289 + 0.5 = 6.922616289 x = 6.922616289 Simplifying x = 6.922616289Subproblem 2
x + -0.5 = -6.422616289 Simplifying x + -0.5 = -6.422616289 Reorder the terms: -0.5 + x = -6.422616289 Solving -0.5 + x = -6.422616289 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 = -6.422616289 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -6.422616289 + 0.5 x = -6.422616289 + 0.5 Combine like terms: -6.422616289 + 0.5 = -5.922616289 x = -5.922616289 Simplifying x = -5.922616289Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.922616289, -5.922616289}Solution
x = {6.922616289, -5.922616289}
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