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Simplifying (4x + -1)(2x + -1) = 2x Reorder the terms: (-1 + 4x)(2x + -1) = 2x Reorder the terms: (-1 + 4x)(-1 + 2x) = 2x Multiply (-1 + 4x) * (-1 + 2x) (-1(-1 + 2x) + 4x * (-1 + 2x)) = 2x ((-1 * -1 + 2x * -1) + 4x * (-1 + 2x)) = 2x ((1 + -2x) + 4x * (-1 + 2x)) = 2x (1 + -2x + (-1 * 4x + 2x * 4x)) = 2x (1 + -2x + (-4x + 8x2)) = 2x Combine like terms: -2x + -4x = -6x (1 + -6x + 8x2) = 2x Solving 1 + -6x + 8x2 = 2x Solving for variable 'x'. Reorder the terms: 1 + -6x + -2x + 8x2 = 2x + -2x Combine like terms: -6x + -2x = -8x 1 + -8x + 8x2 = 2x + -2x Combine like terms: 2x + -2x = 0 1 + -8x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + -1x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -1x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -1x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -1x + x2 = 0 + -0.125 -1x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -1x + x2 = -0.125 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -0.125 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.125 + 0.25 Combine like terms: -0.125 + 0.25 = 0.125 0.25 + -1x + x2 = 0.125 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.125 Calculate the square root of the right side: 0.353553391 Break this problem into two subproblems by setting (x + -0.5) equal to 0.353553391 and -0.353553391.Subproblem 1
x + -0.5 = 0.353553391 Simplifying x + -0.5 = 0.353553391 Reorder the terms: -0.5 + x = 0.353553391 Solving -0.5 + x = 0.353553391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.353553391 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.353553391 + 0.5 x = 0.353553391 + 0.5 Combine like terms: 0.353553391 + 0.5 = 0.853553391 x = 0.853553391 Simplifying x = 0.853553391Subproblem 2
x + -0.5 = -0.353553391 Simplifying x + -0.5 = -0.353553391 Reorder the terms: -0.5 + x = -0.353553391 Solving -0.5 + x = -0.353553391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.353553391 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.353553391 + 0.5 x = -0.353553391 + 0.5 Combine like terms: -0.353553391 + 0.5 = 0.146446609 x = 0.146446609 Simplifying x = 0.146446609Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.853553391, 0.146446609}
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