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Simplifying (8 + -1x)(6 + -1x) = 40 Multiply (8 + -1x) * (6 + -1x) (8(6 + -1x) + -1x * (6 + -1x)) = 40 ((6 * 8 + -1x * 8) + -1x * (6 + -1x)) = 40 ((48 + -8x) + -1x * (6 + -1x)) = 40 (48 + -8x + (6 * -1x + -1x * -1x)) = 40 (48 + -8x + (-6x + 1x2)) = 40 Combine like terms: -8x + -6x = -14x (48 + -14x + 1x2) = 40 Solving 48 + -14x + 1x2 = 40 Solving for variable 'x'. Reorder the terms: 48 + -40 + -14x + 1x2 = 40 + -40 Combine like terms: 48 + -40 = 8 8 + -14x + 1x2 = 40 + -40 Combine like terms: 40 + -40 = 0 8 + -14x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -14x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -14x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -14x + x2 = 0 + -8 -14x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -14x + x2 = -8 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -8 + 49 Reorder the terms: 49 + -14x + x2 = -8 + 49 Combine like terms: -8 + 49 = 41 49 + -14x + x2 = 41 Factor a perfect square on the left side: (x + -7)(x + -7) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (x + -7) equal to 6.403124237 and -6.403124237.Subproblem 1
x + -7 = 6.403124237 Simplifying x + -7 = 6.403124237 Reorder the terms: -7 + x = 6.403124237 Solving -7 + x = 6.403124237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 6.403124237 + 7 Combine like terms: -7 + 7 = 0 0 + x = 6.403124237 + 7 x = 6.403124237 + 7 Combine like terms: 6.403124237 + 7 = 13.403124237 x = 13.403124237 Simplifying x = 13.403124237Subproblem 2
x + -7 = -6.403124237 Simplifying x + -7 = -6.403124237 Reorder the terms: -7 + x = -6.403124237 Solving -7 + x = -6.403124237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -6.403124237 + 7 Combine like terms: -7 + 7 = 0 0 + x = -6.403124237 + 7 x = -6.403124237 + 7 Combine like terms: -6.403124237 + 7 = 0.596875763 x = 0.596875763 Simplifying x = 0.596875763Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.403124237, 0.596875763}
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