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Simplifying x2 + -165 + x = 0 Reorder the terms: -165 + x + x2 = 0 Solving -165 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '165' to each side of the equation. -165 + x + 165 + x2 = 0 + 165 Reorder the terms: -165 + 165 + x + x2 = 0 + 165 Combine like terms: -165 + 165 = 0 0 + x + x2 = 0 + 165 x + x2 = 0 + 165 Combine like terms: 0 + 165 = 165 x + x2 = 165 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 = 165 + 0.25 Reorder the terms: 0.25 + x + x2 = 165 + 0.25 Combine like terms: 165 + 0.25 = 165.25 0.25 + x + x2 = 165.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 165.25 Calculate the square root of the right side: 12.854960132 Break this problem into two subproblems by setting (x + 0.5) equal to 12.854960132 and -12.854960132.Subproblem 1
x + 0.5 = 12.854960132 Simplifying x + 0.5 = 12.854960132 Reorder the terms: 0.5 + x = 12.854960132 Solving 0.5 + x = 12.854960132 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 = 12.854960132 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 12.854960132 + -0.5 x = 12.854960132 + -0.5 Combine like terms: 12.854960132 + -0.5 = 12.354960132 x = 12.354960132 Simplifying x = 12.354960132Subproblem 2
x + 0.5 = -12.854960132 Simplifying x + 0.5 = -12.854960132 Reorder the terms: 0.5 + x = -12.854960132 Solving 0.5 + x = -12.854960132 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 = -12.854960132 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -12.854960132 + -0.5 x = -12.854960132 + -0.5 Combine like terms: -12.854960132 + -0.5 = -13.354960132 x = -13.354960132 Simplifying x = -13.354960132Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.354960132, -13.354960132}
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