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Simplifying x2 + x + -186 = 0 Reorder the terms: -186 + x + x2 = 0 Solving -186 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '186' to each side of the equation. -186 + x + 186 + x2 = 0 + 186 Reorder the terms: -186 + 186 + x + x2 = 0 + 186 Combine like terms: -186 + 186 = 0 0 + x + x2 = 0 + 186 x + x2 = 0 + 186 Combine like terms: 0 + 186 = 186 x + x2 = 186 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 = 186 + 0.25 Reorder the terms: 0.25 + x + x2 = 186 + 0.25 Combine like terms: 186 + 0.25 = 186.25 0.25 + x + x2 = 186.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 186.25 Calculate the square root of the right side: 13.647344064 Break this problem into two subproblems by setting (x + 0.5) equal to 13.647344064 and -13.647344064.Subproblem 1
x + 0.5 = 13.647344064 Simplifying x + 0.5 = 13.647344064 Reorder the terms: 0.5 + x = 13.647344064 Solving 0.5 + x = 13.647344064 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 = 13.647344064 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 13.647344064 + -0.5 x = 13.647344064 + -0.5 Combine like terms: 13.647344064 + -0.5 = 13.147344064 x = 13.147344064 Simplifying x = 13.147344064Subproblem 2
x + 0.5 = -13.647344064 Simplifying x + 0.5 = -13.647344064 Reorder the terms: 0.5 + x = -13.647344064 Solving 0.5 + x = -13.647344064 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 = -13.647344064 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -13.647344064 + -0.5 x = -13.647344064 + -0.5 Combine like terms: -13.647344064 + -0.5 = -14.147344064 x = -14.147344064 Simplifying x = -14.147344064Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.147344064, -14.147344064}
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