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Simplifying (6 + -1x)(2 + -1x) + 1 = 0 Multiply (6 + -1x) * (2 + -1x) (6(2 + -1x) + -1x * (2 + -1x)) + 1 = 0 ((2 * 6 + -1x * 6) + -1x * (2 + -1x)) + 1 = 0 ((12 + -6x) + -1x * (2 + -1x)) + 1 = 0 (12 + -6x + (2 * -1x + -1x * -1x)) + 1 = 0 (12 + -6x + (-2x + 1x2)) + 1 = 0 Combine like terms: -6x + -2x = -8x (12 + -8x + 1x2) + 1 = 0 Reorder the terms: 12 + 1 + -8x + 1x2 = 0 Combine like terms: 12 + 1 = 13 13 + -8x + 1x2 = 0 Solving 13 + -8x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -8x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + -8x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -8x + x2 = 0 + -13 -8x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 -8x + x2 = -13 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -13 + 16 Reorder the terms: 16 + -8x + x2 = -13 + 16 Combine like terms: -13 + 16 = 3 16 + -8x + x2 = 3 Factor a perfect square on the left side: (x + -4)(x + -4) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + -4) equal to 1.732050808 and -1.732050808.Subproblem 1
x + -4 = 1.732050808 Simplifying x + -4 = 1.732050808 Reorder the terms: -4 + x = 1.732050808 Solving -4 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 1.732050808 + 4 Combine like terms: -4 + 4 = 0 0 + x = 1.732050808 + 4 x = 1.732050808 + 4 Combine like terms: 1.732050808 + 4 = 5.732050808 x = 5.732050808 Simplifying x = 5.732050808Subproblem 2
x + -4 = -1.732050808 Simplifying x + -4 = -1.732050808 Reorder the terms: -4 + x = -1.732050808 Solving -4 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -1.732050808 + 4 Combine like terms: -4 + 4 = 0 0 + x = -1.732050808 + 4 x = -1.732050808 + 4 Combine like terms: -1.732050808 + 4 = 2.267949192 x = 2.267949192 Simplifying x = 2.267949192Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.732050808, 2.267949192}
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