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Simplifying x2 + 3.61x + 3.24 = 0 Reorder the terms: 3.24 + 3.61x + x2 = 0 Solving 3.24 + 3.61x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3.24' to each side of the equation. 3.24 + 3.61x + -3.24 + x2 = 0 + -3.24 Reorder the terms: 3.24 + -3.24 + 3.61x + x2 = 0 + -3.24 Combine like terms: 3.24 + -3.24 = 0.00 0.00 + 3.61x + x2 = 0 + -3.24 3.61x + x2 = 0 + -3.24 Combine like terms: 0 + -3.24 = -3.24 3.61x + x2 = -3.24 The x term is 3.61x. Take half its coefficient (1.805). Square it (3.258025) and add it to both sides. Add '3.258025' to each side of the equation. 3.61x + 3.258025 + x2 = -3.24 + 3.258025 Reorder the terms: 3.258025 + 3.61x + x2 = -3.24 + 3.258025 Combine like terms: -3.24 + 3.258025 = 0.018025 3.258025 + 3.61x + x2 = 0.018025 Factor a perfect square on the left side: (x + 1.805)(x + 1.805) = 0.018025 Calculate the square root of the right side: 0.134257216 Break this problem into two subproblems by setting (x + 1.805) equal to 0.134257216 and -0.134257216.Subproblem 1
x + 1.805 = 0.134257216 Simplifying x + 1.805 = 0.134257216 Reorder the terms: 1.805 + x = 0.134257216 Solving 1.805 + x = 0.134257216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.805' to each side of the equation. 1.805 + -1.805 + x = 0.134257216 + -1.805 Combine like terms: 1.805 + -1.805 = 0.000 0.000 + x = 0.134257216 + -1.805 x = 0.134257216 + -1.805 Combine like terms: 0.134257216 + -1.805 = -1.670742784 x = -1.670742784 Simplifying x = -1.670742784Subproblem 2
x + 1.805 = -0.134257216 Simplifying x + 1.805 = -0.134257216 Reorder the terms: 1.805 + x = -0.134257216 Solving 1.805 + x = -0.134257216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.805' to each side of the equation. 1.805 + -1.805 + x = -0.134257216 + -1.805 Combine like terms: 1.805 + -1.805 = 0.000 0.000 + x = -0.134257216 + -1.805 x = -0.134257216 + -1.805 Combine like terms: -0.134257216 + -1.805 = -1.939257216 x = -1.939257216 Simplifying x = -1.939257216Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.670742784, -1.939257216}
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