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Simplifying (3x + 24)(2x + 7) = 2 Reorder the terms: (24 + 3x)(2x + 7) = 2 Reorder the terms: (24 + 3x)(7 + 2x) = 2 Multiply (24 + 3x) * (7 + 2x) (24(7 + 2x) + 3x * (7 + 2x)) = 2 ((7 * 24 + 2x * 24) + 3x * (7 + 2x)) = 2 ((168 + 48x) + 3x * (7 + 2x)) = 2 (168 + 48x + (7 * 3x + 2x * 3x)) = 2 (168 + 48x + (21x + 6x2)) = 2 Combine like terms: 48x + 21x = 69x (168 + 69x + 6x2) = 2 Solving 168 + 69x + 6x2 = 2 Solving for variable 'x'. Reorder the terms: 168 + -2 + 69x + 6x2 = 2 + -2 Combine like terms: 168 + -2 = 166 166 + 69x + 6x2 = 2 + -2 Combine like terms: 2 + -2 = 0 166 + 69x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 27.66666667 + 11.5x + x2 = 0 Move the constant term to the right: Add '-27.66666667' to each side of the equation. 27.66666667 + 11.5x + -27.66666667 + x2 = 0 + -27.66666667 Reorder the terms: 27.66666667 + -27.66666667 + 11.5x + x2 = 0 + -27.66666667 Combine like terms: 27.66666667 + -27.66666667 = 0.00000000 0.00000000 + 11.5x + x2 = 0 + -27.66666667 11.5x + x2 = 0 + -27.66666667 Combine like terms: 0 + -27.66666667 = -27.66666667 11.5x + x2 = -27.66666667 The x term is 11.5x. Take half its coefficient (5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. 11.5x + 33.0625 + x2 = -27.66666667 + 33.0625 Reorder the terms: 33.0625 + 11.5x + x2 = -27.66666667 + 33.0625 Combine like terms: -27.66666667 + 33.0625 = 5.39583333 33.0625 + 11.5x + x2 = 5.39583333 Factor a perfect square on the left side: (x + 5.75)(x + 5.75) = 5.39583333 Calculate the square root of the right side: 2.32289331 Break this problem into two subproblems by setting (x + 5.75) equal to 2.32289331 and -2.32289331.Subproblem 1
x + 5.75 = 2.32289331 Simplifying x + 5.75 = 2.32289331 Reorder the terms: 5.75 + x = 2.32289331 Solving 5.75 + x = 2.32289331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = 2.32289331 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = 2.32289331 + -5.75 x = 2.32289331 + -5.75 Combine like terms: 2.32289331 + -5.75 = -3.42710669 x = -3.42710669 Simplifying x = -3.42710669Subproblem 2
x + 5.75 = -2.32289331 Simplifying x + 5.75 = -2.32289331 Reorder the terms: 5.75 + x = -2.32289331 Solving 5.75 + x = -2.32289331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = -2.32289331 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = -2.32289331 + -5.75 x = -2.32289331 + -5.75 Combine like terms: -2.32289331 + -5.75 = -8.07289331 x = -8.07289331 Simplifying x = -8.07289331Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.42710669, -8.07289331}
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