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Simplifying x2 + 3x + -142 = 0 Reorder the terms: -142 + 3x + x2 = 0 Solving -142 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '142' to each side of the equation. -142 + 3x + 142 + x2 = 0 + 142 Reorder the terms: -142 + 142 + 3x + x2 = 0 + 142 Combine like terms: -142 + 142 = 0 0 + 3x + x2 = 0 + 142 3x + x2 = 0 + 142 Combine like terms: 0 + 142 = 142 3x + x2 = 142 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 = 142 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 142 + 2.25 Combine like terms: 142 + 2.25 = 144.25 2.25 + 3x + x2 = 144.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 144.25 Calculate the square root of the right side: 12.010412149 Break this problem into two subproblems by setting (x + 1.5) equal to 12.010412149 and -12.010412149.Subproblem 1
x + 1.5 = 12.010412149 Simplifying x + 1.5 = 12.010412149 Reorder the terms: 1.5 + x = 12.010412149 Solving 1.5 + x = 12.010412149 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 = 12.010412149 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 12.010412149 + -1.5 x = 12.010412149 + -1.5 Combine like terms: 12.010412149 + -1.5 = 10.510412149 x = 10.510412149 Simplifying x = 10.510412149Subproblem 2
x + 1.5 = -12.010412149 Simplifying x + 1.5 = -12.010412149 Reorder the terms: 1.5 + x = -12.010412149 Solving 1.5 + x = -12.010412149 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 = -12.010412149 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -12.010412149 + -1.5 x = -12.010412149 + -1.5 Combine like terms: -12.010412149 + -1.5 = -13.510412149 x = -13.510412149 Simplifying x = -13.510412149Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.510412149, -13.510412149}
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