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Simplifying x2 + x + 25 = 180 Reorder the terms: 25 + x + x2 = 180 Solving 25 + x + x2 = 180 Solving for variable 'x'. Reorder the terms: 25 + -180 + x + x2 = 180 + -180 Combine like terms: 25 + -180 = -155 -155 + x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -155 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '155' to each side of the equation. -155 + x + 155 + x2 = 0 + 155 Reorder the terms: -155 + 155 + x + x2 = 0 + 155 Combine like terms: -155 + 155 = 0 0 + x + x2 = 0 + 155 x + x2 = 0 + 155 Combine like terms: 0 + 155 = 155 x + x2 = 155 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 = 155 + 0.25 Reorder the terms: 0.25 + x + x2 = 155 + 0.25 Combine like terms: 155 + 0.25 = 155.25 0.25 + x + x2 = 155.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 155.25 Calculate the square root of the right side: 12.459935794 Break this problem into two subproblems by setting (x + 0.5) equal to 12.459935794 and -12.459935794.Subproblem 1
x + 0.5 = 12.459935794 Simplifying x + 0.5 = 12.459935794 Reorder the terms: 0.5 + x = 12.459935794 Solving 0.5 + x = 12.459935794 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 = 12.459935794 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 12.459935794 + -0.5 x = 12.459935794 + -0.5 Combine like terms: 12.459935794 + -0.5 = 11.959935794 x = 11.959935794 Simplifying x = 11.959935794Subproblem 2
x + 0.5 = -12.459935794 Simplifying x + 0.5 = -12.459935794 Reorder the terms: 0.5 + x = -12.459935794 Solving 0.5 + x = -12.459935794 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 = -12.459935794 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -12.459935794 + -0.5 x = -12.459935794 + -0.5 Combine like terms: -12.459935794 + -0.5 = -12.959935794 x = -12.959935794 Simplifying x = -12.959935794Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.959935794, -12.959935794}
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