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Simplifying -1(2x + -3) + 4 = -5x + 2(3x + 5) * x Reorder the terms: -1(-3 + 2x) + 4 = -5x + 2(3x + 5) * x (-3 * -1 + 2x * -1) + 4 = -5x + 2(3x + 5) * x (3 + -2x) + 4 = -5x + 2(3x + 5) * x Reorder the terms: 3 + 4 + -2x = -5x + 2(3x + 5) * x Combine like terms: 3 + 4 = 7 7 + -2x = -5x + 2(3x + 5) * x Reorder the terms: 7 + -2x = -5x + 2(5 + 3x) * x Reorder the terms for easier multiplication: 7 + -2x = -5x + 2x(5 + 3x) 7 + -2x = -5x + (5 * 2x + 3x * 2x) 7 + -2x = -5x + (10x + 6x2) Combine like terms: -5x + 10x = 5x 7 + -2x = 5x + 6x2 Solving 7 + -2x = 5x + 6x2 Solving for variable 'x'. Combine like terms: -2x + -5x = -7x 7 + -7x + -6x2 = 5x + 6x2 + -5x + -6x2 Reorder the terms: 7 + -7x + -6x2 = 5x + -5x + 6x2 + -6x2 Combine like terms: 5x + -5x = 0 7 + -7x + -6x2 = 0 + 6x2 + -6x2 7 + -7x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 7 + -7x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -1.166666667 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667x + 1.166666667 + x2 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + 1.166666667x + x2 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + 1.166666667x + x2 = 0 + 1.166666667 1.166666667x + x2 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 1.166666667x + x2 = 1.166666667 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 = 1.166666667 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = 1.166666667 + 0.3402777780 Combine like terms: 1.166666667 + 0.3402777780 = 1.506944445 0.3402777780 + 1.166666667x + x2 = 1.506944445 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 1.506944445 Calculate the square root of the right side: 1.227576655 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 1.227576655 and -1.227576655.Subproblem 1
x + 0.5833333335 = 1.227576655 Simplifying x + 0.5833333335 = 1.227576655 Reorder the terms: 0.5833333335 + x = 1.227576655 Solving 0.5833333335 + x = 1.227576655 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 = 1.227576655 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 1.227576655 + -0.5833333335 x = 1.227576655 + -0.5833333335 Combine like terms: 1.227576655 + -0.5833333335 = 0.6442433215 x = 0.6442433215 Simplifying x = 0.6442433215Subproblem 2
x + 0.5833333335 = -1.227576655 Simplifying x + 0.5833333335 = -1.227576655 Reorder the terms: 0.5833333335 + x = -1.227576655 Solving 0.5833333335 + x = -1.227576655 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 = -1.227576655 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -1.227576655 + -0.5833333335 x = -1.227576655 + -0.5833333335 Combine like terms: -1.227576655 + -0.5833333335 = -1.8109099885 x = -1.8109099885 Simplifying x = -1.8109099885Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6442433215, -1.8109099885}
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