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Simplifying (3X + -4)(X + -1.4142) = 0 Reorder the terms: (-4 + 3X)(X + -1.4142) = 0 Reorder the terms: (-4 + 3X)(-1.4142 + X) = 0 Multiply (-4 + 3X) * (-1.4142 + X) (-4(-1.4142 + X) + 3X * (-1.4142 + X)) = 0 ((-1.4142 * -4 + X * -4) + 3X * (-1.4142 + X)) = 0 ((5.6568 + -4X) + 3X * (-1.4142 + X)) = 0 (5.6568 + -4X + (-1.4142 * 3X + X * 3X)) = 0 (5.6568 + -4X + (-4.2426X + 3X2)) = 0 Combine like terms: -4X + -4.2426X = -8.2426X (5.6568 + -8.2426X + 3X2) = 0 Solving 5.6568 + -8.2426X + 3X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.8856 + -2.747533333X + X2 = 0 Move the constant term to the right: Add '-1.8856' to each side of the equation. 1.8856 + -2.747533333X + -1.8856 + X2 = 0 + -1.8856 Reorder the terms: 1.8856 + -1.8856 + -2.747533333X + X2 = 0 + -1.8856 Combine like terms: 1.8856 + -1.8856 = 0.0000 0.0000 + -2.747533333X + X2 = 0 + -1.8856 -2.747533333X + X2 = 0 + -1.8856 Combine like terms: 0 + -1.8856 = -1.8856 -2.747533333X + X2 = -1.8856 The X term is -2.747533333X. Take half its coefficient (-1.373766667). Square it (1.887234855) and add it to both sides. Add '1.887234855' to each side of the equation. -2.747533333X + 1.887234855 + X2 = -1.8856 + 1.887234855 Reorder the terms: 1.887234855 + -2.747533333X + X2 = -1.8856 + 1.887234855 Combine like terms: -1.8856 + 1.887234855 = 0.001634855 1.887234855 + -2.747533333X + X2 = 0.001634855 Factor a perfect square on the left side: (X + -1.373766667)(X + -1.373766667) = 0.001634855 Calculate the square root of the right side: 0.04043334 Break this problem into two subproblems by setting (X + -1.373766667) equal to 0.04043334 and -0.04043334.Subproblem 1
X + -1.373766667 = 0.04043334 Simplifying X + -1.373766667 = 0.04043334 Reorder the terms: -1.373766667 + X = 0.04043334 Solving -1.373766667 + X = 0.04043334 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.373766667' to each side of the equation. -1.373766667 + 1.373766667 + X = 0.04043334 + 1.373766667 Combine like terms: -1.373766667 + 1.373766667 = 0.000000000 0.000000000 + X = 0.04043334 + 1.373766667 X = 0.04043334 + 1.373766667 Combine like terms: 0.04043334 + 1.373766667 = 1.414200007 X = 1.414200007 Simplifying X = 1.414200007Subproblem 2
X + -1.373766667 = -0.04043334 Simplifying X + -1.373766667 = -0.04043334 Reorder the terms: -1.373766667 + X = -0.04043334 Solving -1.373766667 + X = -0.04043334 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.373766667' to each side of the equation. -1.373766667 + 1.373766667 + X = -0.04043334 + 1.373766667 Combine like terms: -1.373766667 + 1.373766667 = 0.000000000 0.000000000 + X = -0.04043334 + 1.373766667 X = -0.04043334 + 1.373766667 Combine like terms: -0.04043334 + 1.373766667 = 1.333333327 X = 1.333333327 Simplifying X = 1.333333327Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.414200007, 1.333333327}
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