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Simplifying (7 + -1x)(3.5 + -1x) = 18.4 Multiply (7 + -1x) * (3.5 + -1x) (7(3.5 + -1x) + -1x * (3.5 + -1x)) = 18.4 ((3.5 * 7 + -1x * 7) + -1x * (3.5 + -1x)) = 18.4 ((24.5 + -7x) + -1x * (3.5 + -1x)) = 18.4 (24.5 + -7x + (3.5 * -1x + -1x * -1x)) = 18.4 (24.5 + -7x + (-3.5x + 1x2)) = 18.4 Combine like terms: -7x + -3.5x = -10.5x (24.5 + -10.5x + 1x2) = 18.4 Solving 24.5 + -10.5x + 1x2 = 18.4 Solving for variable 'x'. Reorder the terms: 24.5 + -18.4 + -10.5x + 1x2 = 18.4 + -18.4 Combine like terms: 24.5 + -18.4 = 6.1 6.1 + -10.5x + 1x2 = 18.4 + -18.4 Combine like terms: 18.4 + -18.4 = 0.0 6.1 + -10.5x + 1x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '-6.1' to each side of the equation. 6.1 + -10.5x + -6.1 + x2 = 0.0 + -6.1 Reorder the terms: 6.1 + -6.1 + -10.5x + x2 = 0.0 + -6.1 Combine like terms: 6.1 + -6.1 = 0.0 0.0 + -10.5x + x2 = 0.0 + -6.1 -10.5x + x2 = 0.0 + -6.1 Combine like terms: 0.0 + -6.1 = -6.1 -10.5x + x2 = -6.1 The x term is -10.5x. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5x + 27.5625 + x2 = -6.1 + 27.5625 Reorder the terms: 27.5625 + -10.5x + x2 = -6.1 + 27.5625 Combine like terms: -6.1 + 27.5625 = 21.4625 27.5625 + -10.5x + x2 = 21.4625 Factor a perfect square on the left side: (x + -5.25)(x + -5.25) = 21.4625 Calculate the square root of the right side: 4.632763754 Break this problem into two subproblems by setting (x + -5.25) equal to 4.632763754 and -4.632763754.Subproblem 1
x + -5.25 = 4.632763754 Simplifying x + -5.25 = 4.632763754 Reorder the terms: -5.25 + x = 4.632763754 Solving -5.25 + x = 4.632763754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 4.632763754 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 4.632763754 + 5.25 x = 4.632763754 + 5.25 Combine like terms: 4.632763754 + 5.25 = 9.882763754 x = 9.882763754 Simplifying x = 9.882763754Subproblem 2
x + -5.25 = -4.632763754 Simplifying x + -5.25 = -4.632763754 Reorder the terms: -5.25 + x = -4.632763754 Solving -5.25 + x = -4.632763754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -4.632763754 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -4.632763754 + 5.25 x = -4.632763754 + 5.25 Combine like terms: -4.632763754 + 5.25 = 0.617236246 x = 0.617236246 Simplifying x = 0.617236246Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.882763754, 0.617236246}
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