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Simplifying (5x + -1)(2x + 1) = 2x Reorder the terms: (-1 + 5x)(2x + 1) = 2x Reorder the terms: (-1 + 5x)(1 + 2x) = 2x Multiply (-1 + 5x) * (1 + 2x) (-1(1 + 2x) + 5x * (1 + 2x)) = 2x ((1 * -1 + 2x * -1) + 5x * (1 + 2x)) = 2x ((-1 + -2x) + 5x * (1 + 2x)) = 2x (-1 + -2x + (1 * 5x + 2x * 5x)) = 2x (-1 + -2x + (5x + 10x2)) = 2x Combine like terms: -2x + 5x = 3x (-1 + 3x + 10x2) = 2x Solving -1 + 3x + 10x2 = 2x Solving for variable 'x'. Reorder the terms: -1 + 3x + -2x + 10x2 = 2x + -2x Combine like terms: 3x + -2x = 1x -1 + 1x + 10x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -1 + 1x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.1 + 0.1x + x2 = 0.0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + 0.1x + 0.1 + x2 = 0.0 + 0.1 Reorder the terms: -0.1 + 0.1 + 0.1x + x2 = 0.0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 0.1x + x2 = 0.0 + 0.1 0.1x + x2 = 0.0 + 0.1 Combine like terms: 0.0 + 0.1 = 0.1 0.1x + x2 = 0.1 The x term is 0.1x. Take half its coefficient (0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. 0.1x + 0.0025 + x2 = 0.1 + 0.0025 Reorder the terms: 0.0025 + 0.1x + x2 = 0.1 + 0.0025 Combine like terms: 0.1 + 0.0025 = 0.1025 0.0025 + 0.1x + x2 = 0.1025 Factor a perfect square on the left side: (x + 0.05)(x + 0.05) = 0.1025 Calculate the square root of the right side: 0.320156212 Break this problem into two subproblems by setting (x + 0.05) equal to 0.320156212 and -0.320156212.Subproblem 1
x + 0.05 = 0.320156212 Simplifying x + 0.05 = 0.320156212 Reorder the terms: 0.05 + x = 0.320156212 Solving 0.05 + x = 0.320156212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = 0.320156212 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = 0.320156212 + -0.05 x = 0.320156212 + -0.05 Combine like terms: 0.320156212 + -0.05 = 0.270156212 x = 0.270156212 Simplifying x = 0.270156212Subproblem 2
x + 0.05 = -0.320156212 Simplifying x + 0.05 = -0.320156212 Reorder the terms: 0.05 + x = -0.320156212 Solving 0.05 + x = -0.320156212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = -0.320156212 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = -0.320156212 + -0.05 x = -0.320156212 + -0.05 Combine like terms: -0.320156212 + -0.05 = -0.370156212 x = -0.370156212 Simplifying x = -0.370156212Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.270156212, -0.370156212}
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