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Simplifying (4x + 3) + (2x + -7)(3x + 5) = 0 Reorder the terms: (3 + 4x) + (2x + -7)(3x + 5) = 0 Remove parenthesis around (3 + 4x) 3 + 4x + (2x + -7)(3x + 5) = 0 Reorder the terms: 3 + 4x + (-7 + 2x)(3x + 5) = 0 Reorder the terms: 3 + 4x + (-7 + 2x)(5 + 3x) = 0 Multiply (-7 + 2x) * (5 + 3x) 3 + 4x + (-7(5 + 3x) + 2x * (5 + 3x)) = 0 3 + 4x + ((5 * -7 + 3x * -7) + 2x * (5 + 3x)) = 0 3 + 4x + ((-35 + -21x) + 2x * (5 + 3x)) = 0 3 + 4x + (-35 + -21x + (5 * 2x + 3x * 2x)) = 0 3 + 4x + (-35 + -21x + (10x + 6x2)) = 0 Combine like terms: -21x + 10x = -11x 3 + 4x + (-35 + -11x + 6x2) = 0 Reorder the terms: 3 + -35 + 4x + -11x + 6x2 = 0 Combine like terms: 3 + -35 = -32 -32 + 4x + -11x + 6x2 = 0 Combine like terms: 4x + -11x = -7x -32 + -7x + 6x2 = 0 Solving -32 + -7x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -5.333333333 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + -1.166666667x + 5.333333333 + x2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + -1.166666667x + x2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + -1.166666667x + x2 = 0 + 5.333333333 -1.166666667x + x2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 -1.166666667x + x2 = 5.333333333 The x term is -1.166666667x. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667x + 0.3402777780 + x2 = 5.333333333 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 5.333333333 + 0.3402777780 Combine like terms: 5.333333333 + 0.3402777780 = 5.673611111 0.3402777780 + -1.166666667x + x2 = 5.673611111 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 5.673611111 Calculate the square root of the right side: 2.381934321 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 2.381934321 and -2.381934321.Subproblem 1
x + -0.5833333335 = 2.381934321 Simplifying x + -0.5833333335 = 2.381934321 Reorder the terms: -0.5833333335 + x = 2.381934321 Solving -0.5833333335 + x = 2.381934321 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = 2.381934321 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 2.381934321 + 0.5833333335 x = 2.381934321 + 0.5833333335 Combine like terms: 2.381934321 + 0.5833333335 = 2.9652676545 x = 2.9652676545 Simplifying x = 2.9652676545Subproblem 2
x + -0.5833333335 = -2.381934321 Simplifying x + -0.5833333335 = -2.381934321 Reorder the terms: -0.5833333335 + x = -2.381934321 Solving -0.5833333335 + x = -2.381934321 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = -2.381934321 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -2.381934321 + 0.5833333335 x = -2.381934321 + 0.5833333335 Combine like terms: -2.381934321 + 0.5833333335 = -1.7986009875 x = -1.7986009875 Simplifying x = -1.7986009875Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.9652676545, -1.7986009875}
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