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Simplifying (1.00 + -1x)(2.00 + -1x) = 0.680 Multiply (1.00 + -1x) * (2.00 + -1x) (1.00(2.00 + -1x) + -1x * (2.00 + -1x)) = 0.680 ((2.00 * 1.00 + -1x * 1.00) + -1x * (2.00 + -1x)) = 0.680 ((2 + -1x) + -1x * (2.00 + -1x)) = 0.680 (2 + -1x + (2.00 * -1x + -1x * -1x)) = 0.680 (2 + -1x + (-2x + 1x2)) = 0.680 Combine like terms: -1x + -2x = -3x (2 + -3x + 1x2) = 0.680 Solving 2 + -3x + 1x2 = 0.680 Solving for variable 'x'. Reorder the terms: 2 + -0.680 + -3x + 1x2 = 0.680 + -0.680 Combine like terms: 2 + -0.680 = 1.32 1.32 + -3x + 1x2 = 0.680 + -0.680 Combine like terms: 0.680 + -0.680 = 0.000 1.32 + -3x + 1x2 = 0.000 Begin completing the square. Move the constant term to the right: Add '-1.32' to each side of the equation. 1.32 + -3x + -1.32 + x2 = 0.000 + -1.32 Reorder the terms: 1.32 + -1.32 + -3x + x2 = 0.000 + -1.32 Combine like terms: 1.32 + -1.32 = 0.00 0.00 + -3x + x2 = 0.000 + -1.32 -3x + x2 = 0.000 + -1.32 Combine like terms: 0.000 + -1.32 = -1.32 -3x + x2 = -1.32 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 = -1.32 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -1.32 + 2.25 Combine like terms: -1.32 + 2.25 = 0.93 2.25 + -3x + x2 = 0.93 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 0.93 Calculate the square root of the right side: 0.964365076 Break this problem into two subproblems by setting (x + -1.5) equal to 0.964365076 and -0.964365076.Subproblem 1
x + -1.5 = 0.964365076 Simplifying x + -1.5 = 0.964365076 Reorder the terms: -1.5 + x = 0.964365076 Solving -1.5 + x = 0.964365076 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 = 0.964365076 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 0.964365076 + 1.5 x = 0.964365076 + 1.5 Combine like terms: 0.964365076 + 1.5 = 2.464365076 x = 2.464365076 Simplifying x = 2.464365076Subproblem 2
x + -1.5 = -0.964365076 Simplifying x + -1.5 = -0.964365076 Reorder the terms: -1.5 + x = -0.964365076 Solving -1.5 + x = -0.964365076 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 = -0.964365076 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -0.964365076 + 1.5 x = -0.964365076 + 1.5 Combine like terms: -0.964365076 + 1.5 = 0.535634924 x = 0.535634924 Simplifying x = 0.535634924Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.464365076, 0.535634924}
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