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Simplifying (5x + -6)(3x + 5) = 142 Reorder the terms: (-6 + 5x)(3x + 5) = 142 Reorder the terms: (-6 + 5x)(5 + 3x) = 142 Multiply (-6 + 5x) * (5 + 3x) (-6(5 + 3x) + 5x * (5 + 3x)) = 142 ((5 * -6 + 3x * -6) + 5x * (5 + 3x)) = 142 ((-30 + -18x) + 5x * (5 + 3x)) = 142 (-30 + -18x + (5 * 5x + 3x * 5x)) = 142 (-30 + -18x + (25x + 15x2)) = 142 Combine like terms: -18x + 25x = 7x (-30 + 7x + 15x2) = 142 Solving -30 + 7x + 15x2 = 142 Solving for variable 'x'. Reorder the terms: -30 + -142 + 7x + 15x2 = 142 + -142 Combine like terms: -30 + -142 = -172 -172 + 7x + 15x2 = 142 + -142 Combine like terms: 142 + -142 = 0 -172 + 7x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -11.46666667 + 0.4666666667x + x2 = 0 Move the constant term to the right: Add '11.46666667' to each side of the equation. -11.46666667 + 0.4666666667x + 11.46666667 + x2 = 0 + 11.46666667 Reorder the terms: -11.46666667 + 11.46666667 + 0.4666666667x + x2 = 0 + 11.46666667 Combine like terms: -11.46666667 + 11.46666667 = 0.00000000 0.00000000 + 0.4666666667x + x2 = 0 + 11.46666667 0.4666666667x + x2 = 0 + 11.46666667 Combine like terms: 0 + 11.46666667 = 11.46666667 0.4666666667x + x2 = 11.46666667 The x term is 0.4666666667x. Take half its coefficient (0.2333333334). Square it (0.05444444448) and add it to both sides. Add '0.05444444448' to each side of the equation. 0.4666666667x + 0.05444444448 + x2 = 11.46666667 + 0.05444444448 Reorder the terms: 0.05444444448 + 0.4666666667x + x2 = 11.46666667 + 0.05444444448 Combine like terms: 11.46666667 + 0.05444444448 = 11.52111111448 0.05444444448 + 0.4666666667x + x2 = 11.52111111448 Factor a perfect square on the left side: (x + 0.2333333334)(x + 0.2333333334) = 11.52111111448 Calculate the square root of the right side: 3.394276228 Break this problem into two subproblems by setting (x + 0.2333333334) equal to 3.394276228 and -3.394276228.Subproblem 1
x + 0.2333333334 = 3.394276228 Simplifying x + 0.2333333334 = 3.394276228 Reorder the terms: 0.2333333334 + x = 3.394276228 Solving 0.2333333334 + x = 3.394276228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2333333334' to each side of the equation. 0.2333333334 + -0.2333333334 + x = 3.394276228 + -0.2333333334 Combine like terms: 0.2333333334 + -0.2333333334 = 0.0000000000 0.0000000000 + x = 3.394276228 + -0.2333333334 x = 3.394276228 + -0.2333333334 Combine like terms: 3.394276228 + -0.2333333334 = 3.1609428946 x = 3.1609428946 Simplifying x = 3.1609428946Subproblem 2
x + 0.2333333334 = -3.394276228 Simplifying x + 0.2333333334 = -3.394276228 Reorder the terms: 0.2333333334 + x = -3.394276228 Solving 0.2333333334 + x = -3.394276228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2333333334' to each side of the equation. 0.2333333334 + -0.2333333334 + x = -3.394276228 + -0.2333333334 Combine like terms: 0.2333333334 + -0.2333333334 = 0.0000000000 0.0000000000 + x = -3.394276228 + -0.2333333334 x = -3.394276228 + -0.2333333334 Combine like terms: -3.394276228 + -0.2333333334 = -3.6276095614 x = -3.6276095614 Simplifying x = -3.6276095614Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.1609428946, -3.6276095614}
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