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Simplifying x2 + 3x + -207 = 0 Reorder the terms: -207 + 3x + x2 = 0 Solving -207 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '207' to each side of the equation. -207 + 3x + 207 + x2 = 0 + 207 Reorder the terms: -207 + 207 + 3x + x2 = 0 + 207 Combine like terms: -207 + 207 = 0 0 + 3x + x2 = 0 + 207 3x + x2 = 0 + 207 Combine like terms: 0 + 207 = 207 3x + x2 = 207 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 207 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 207 + 2.25 Combine like terms: 207 + 2.25 = 209.25 2.25 + 3x + x2 = 209.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 209.25 Calculate the square root of the right side: 14.465476141 Break this problem into two subproblems by setting (x + 1.5) equal to 14.465476141 and -14.465476141.Subproblem 1
x + 1.5 = 14.465476141 Simplifying x + 1.5 = 14.465476141 Reorder the terms: 1.5 + x = 14.465476141 Solving 1.5 + x = 14.465476141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 14.465476141 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 14.465476141 + -1.5 x = 14.465476141 + -1.5 Combine like terms: 14.465476141 + -1.5 = 12.965476141 x = 12.965476141 Simplifying x = 12.965476141Subproblem 2
x + 1.5 = -14.465476141 Simplifying x + 1.5 = -14.465476141 Reorder the terms: 1.5 + x = -14.465476141 Solving 1.5 + x = -14.465476141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -14.465476141 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -14.465476141 + -1.5 x = -14.465476141 + -1.5 Combine like terms: -14.465476141 + -1.5 = -15.965476141 x = -15.965476141 Simplifying x = -15.965476141Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.965476141, -15.965476141}
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