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Simplifying (6x + 4)(4x + 7.05) = 66 Reorder the terms: (4 + 6x)(4x + 7.05) = 66 Reorder the terms: (4 + 6x)(7.05 + 4x) = 66 Multiply (4 + 6x) * (7.05 + 4x) (4(7.05 + 4x) + 6x * (7.05 + 4x)) = 66 ((7.05 * 4 + 4x * 4) + 6x * (7.05 + 4x)) = 66 ((28.2 + 16x) + 6x * (7.05 + 4x)) = 66 (28.2 + 16x + (7.05 * 6x + 4x * 6x)) = 66 (28.2 + 16x + (42.3x + 24x2)) = 66 Combine like terms: 16x + 42.3x = 58.3x (28.2 + 58.3x + 24x2) = 66 Solving 28.2 + 58.3x + 24x2 = 66 Solving for variable 'x'. Reorder the terms: 28.2 + -66 + 58.3x + 24x2 = 66 + -66 Combine like terms: 28.2 + -66 = -37.8 -37.8 + 58.3x + 24x2 = 66 + -66 Combine like terms: 66 + -66 = 0 -37.8 + 58.3x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -1.575 + 2.429166667x + x2 = 0 Move the constant term to the right: Add '1.575' to each side of the equation. -1.575 + 2.429166667x + 1.575 + x2 = 0 + 1.575 Reorder the terms: -1.575 + 1.575 + 2.429166667x + x2 = 0 + 1.575 Combine like terms: -1.575 + 1.575 = 0.000 0.000 + 2.429166667x + x2 = 0 + 1.575 2.429166667x + x2 = 0 + 1.575 Combine like terms: 0 + 1.575 = 1.575 2.429166667x + x2 = 1.575 The x term is 2.429166667x. Take half its coefficient (1.214583334). Square it (1.475212675) and add it to both sides. Add '1.475212675' to each side of the equation. 2.429166667x + 1.475212675 + x2 = 1.575 + 1.475212675 Reorder the terms: 1.475212675 + 2.429166667x + x2 = 1.575 + 1.475212675 Combine like terms: 1.575 + 1.475212675 = 3.050212675 1.475212675 + 2.429166667x + x2 = 3.050212675 Factor a perfect square on the left side: (x + 1.214583334)(x + 1.214583334) = 3.050212675 Calculate the square root of the right side: 1.746485807 Break this problem into two subproblems by setting (x + 1.214583334) equal to 1.746485807 and -1.746485807.Subproblem 1
x + 1.214583334 = 1.746485807 Simplifying x + 1.214583334 = 1.746485807 Reorder the terms: 1.214583334 + x = 1.746485807 Solving 1.214583334 + x = 1.746485807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.214583334' to each side of the equation. 1.214583334 + -1.214583334 + x = 1.746485807 + -1.214583334 Combine like terms: 1.214583334 + -1.214583334 = 0.000000000 0.000000000 + x = 1.746485807 + -1.214583334 x = 1.746485807 + -1.214583334 Combine like terms: 1.746485807 + -1.214583334 = 0.531902473 x = 0.531902473 Simplifying x = 0.531902473Subproblem 2
x + 1.214583334 = -1.746485807 Simplifying x + 1.214583334 = -1.746485807 Reorder the terms: 1.214583334 + x = -1.746485807 Solving 1.214583334 + x = -1.746485807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.214583334' to each side of the equation. 1.214583334 + -1.214583334 + x = -1.746485807 + -1.214583334 Combine like terms: 1.214583334 + -1.214583334 = 0.000000000 0.000000000 + x = -1.746485807 + -1.214583334 x = -1.746485807 + -1.214583334 Combine like terms: -1.746485807 + -1.214583334 = -2.961069141 x = -2.961069141 Simplifying x = -2.961069141Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.531902473, -2.961069141}
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