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Simplifying 2x(3x + -1) = 5x + 1 Reorder the terms: 2x(-1 + 3x) = 5x + 1 (-1 * 2x + 3x * 2x) = 5x + 1 (-2x + 6x2) = 5x + 1 Reorder the terms: -2x + 6x2 = 1 + 5x Solving -2x + 6x2 = 1 + 5x Solving for variable 'x'. Reorder the terms: -1 + -2x + -5x + 6x2 = 1 + 5x + -1 + -5x Combine like terms: -2x + -5x = -7x -1 + -7x + 6x2 = 1 + 5x + -1 + -5x Reorder the terms: -1 + -7x + 6x2 = 1 + -1 + 5x + -5x Combine like terms: 1 + -1 = 0 -1 + -7x + 6x2 = 0 + 5x + -5x -1 + -7x + 6x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -1 + -7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.1666666667 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + -1.166666667x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + -1.166666667x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + -1.166666667x + x2 = 0 + 0.1666666667 -1.166666667x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 -1.166666667x + x2 = 0.1666666667 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 = 0.1666666667 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 0.1666666667 + 0.3402777780 Combine like terms: 0.1666666667 + 0.3402777780 = 0.5069444447 0.3402777780 + -1.166666667x + x2 = 0.5069444447 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 0.5069444447 Calculate the square root of the right side: 0.712000312 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 0.712000312 and -0.712000312.Subproblem 1
x + -0.5833333335 = 0.712000312 Simplifying x + -0.5833333335 = 0.712000312 Reorder the terms: -0.5833333335 + x = 0.712000312 Solving -0.5833333335 + x = 0.712000312 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 = 0.712000312 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 0.712000312 + 0.5833333335 x = 0.712000312 + 0.5833333335 Combine like terms: 0.712000312 + 0.5833333335 = 1.2953336455 x = 1.2953336455 Simplifying x = 1.2953336455Subproblem 2
x + -0.5833333335 = -0.712000312 Simplifying x + -0.5833333335 = -0.712000312 Reorder the terms: -0.5833333335 + x = -0.712000312 Solving -0.5833333335 + x = -0.712000312 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 = -0.712000312 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -0.712000312 + 0.5833333335 x = -0.712000312 + 0.5833333335 Combine like terms: -0.712000312 + 0.5833333335 = -0.1286669785 x = -0.1286669785 Simplifying x = -0.1286669785Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2953336455, -0.1286669785}
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