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Simplifying (2x + 6)(4x + 7) = 6x + 13 Reorder the terms: (6 + 2x)(4x + 7) = 6x + 13 Reorder the terms: (6 + 2x)(7 + 4x) = 6x + 13 Multiply (6 + 2x) * (7 + 4x) (6(7 + 4x) + 2x * (7 + 4x)) = 6x + 13 ((7 * 6 + 4x * 6) + 2x * (7 + 4x)) = 6x + 13 ((42 + 24x) + 2x * (7 + 4x)) = 6x + 13 (42 + 24x + (7 * 2x + 4x * 2x)) = 6x + 13 (42 + 24x + (14x + 8x2)) = 6x + 13 Combine like terms: 24x + 14x = 38x (42 + 38x + 8x2) = 6x + 13 Reorder the terms: 42 + 38x + 8x2 = 13 + 6x Solving 42 + 38x + 8x2 = 13 + 6x Solving for variable 'x'. Reorder the terms: 42 + -13 + 38x + -6x + 8x2 = 13 + 6x + -13 + -6x Combine like terms: 42 + -13 = 29 29 + 38x + -6x + 8x2 = 13 + 6x + -13 + -6x Combine like terms: 38x + -6x = 32x 29 + 32x + 8x2 = 13 + 6x + -13 + -6x Reorder the terms: 29 + 32x + 8x2 = 13 + -13 + 6x + -6x Combine like terms: 13 + -13 = 0 29 + 32x + 8x2 = 0 + 6x + -6x 29 + 32x + 8x2 = 6x + -6x Combine like terms: 6x + -6x = 0 29 + 32x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 3.625 + 4x + x2 = 0 Move the constant term to the right: Add '-3.625' to each side of the equation. 3.625 + 4x + -3.625 + x2 = 0 + -3.625 Reorder the terms: 3.625 + -3.625 + 4x + x2 = 0 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + 4x + x2 = 0 + -3.625 4x + x2 = 0 + -3.625 Combine like terms: 0 + -3.625 = -3.625 4x + x2 = -3.625 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -3.625 + 4 Reorder the terms: 4 + 4x + x2 = -3.625 + 4 Combine like terms: -3.625 + 4 = 0.375 4 + 4x + x2 = 0.375 Factor a perfect square on the left side: (x + 2)(x + 2) = 0.375 Calculate the square root of the right side: 0.612372436 Break this problem into two subproblems by setting (x + 2) equal to 0.612372436 and -0.612372436.Subproblem 1
x + 2 = 0.612372436 Simplifying x + 2 = 0.612372436 Reorder the terms: 2 + x = 0.612372436 Solving 2 + x = 0.612372436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0.612372436 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0.612372436 + -2 x = 0.612372436 + -2 Combine like terms: 0.612372436 + -2 = -1.387627564 x = -1.387627564 Simplifying x = -1.387627564Subproblem 2
x + 2 = -0.612372436 Simplifying x + 2 = -0.612372436 Reorder the terms: 2 + x = -0.612372436 Solving 2 + x = -0.612372436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -0.612372436 + -2 Combine like terms: 2 + -2 = 0 0 + x = -0.612372436 + -2 x = -0.612372436 + -2 Combine like terms: -0.612372436 + -2 = -2.612372436 x = -2.612372436 Simplifying x = -2.612372436Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.387627564, -2.612372436}
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