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Simplifying x2 + 85 = 189 + -1x Reorder the terms: 85 + x2 = 189 + -1x Solving 85 + x2 = 189 + -1x Solving for variable 'x'. Reorder the terms: 85 + -189 + x + x2 = 189 + -1x + -189 + x Combine like terms: 85 + -189 = -104 -104 + x + x2 = 189 + -1x + -189 + x Reorder the terms: -104 + x + x2 = 189 + -189 + -1x + x Combine like terms: 189 + -189 = 0 -104 + x + x2 = 0 + -1x + x -104 + x + x2 = -1x + x Combine like terms: -1x + x = 0 -104 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '104' to each side of the equation. -104 + x + 104 + x2 = 0 + 104 Reorder the terms: -104 + 104 + x + x2 = 0 + 104 Combine like terms: -104 + 104 = 0 0 + x + x2 = 0 + 104 x + x2 = 0 + 104 Combine like terms: 0 + 104 = 104 x + x2 = 104 The x term is x. 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. x + 0.25 + x2 = 104 + 0.25 Reorder the terms: 0.25 + x + x2 = 104 + 0.25 Combine like terms: 104 + 0.25 = 104.25 0.25 + x + x2 = 104.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 104.25 Calculate the square root of the right side: 10.210288928 Break this problem into two subproblems by setting (x + 0.5) equal to 10.210288928 and -10.210288928.Subproblem 1
x + 0.5 = 10.210288928 Simplifying x + 0.5 = 10.210288928 Reorder the terms: 0.5 + x = 10.210288928 Solving 0.5 + x = 10.210288928 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 = 10.210288928 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 10.210288928 + -0.5 x = 10.210288928 + -0.5 Combine like terms: 10.210288928 + -0.5 = 9.710288928 x = 9.710288928 Simplifying x = 9.710288928Subproblem 2
x + 0.5 = -10.210288928 Simplifying x + 0.5 = -10.210288928 Reorder the terms: 0.5 + x = -10.210288928 Solving 0.5 + x = -10.210288928 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 = -10.210288928 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -10.210288928 + -0.5 x = -10.210288928 + -0.5 Combine like terms: -10.210288928 + -0.5 = -10.710288928 x = -10.710288928 Simplifying x = -10.710288928Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.710288928, -10.710288928}
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