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Simplifying (7x + -1)(2x + 1) = 4x Reorder the terms: (-1 + 7x)(2x + 1) = 4x Reorder the terms: (-1 + 7x)(1 + 2x) = 4x Multiply (-1 + 7x) * (1 + 2x) (-1(1 + 2x) + 7x * (1 + 2x)) = 4x ((1 * -1 + 2x * -1) + 7x * (1 + 2x)) = 4x ((-1 + -2x) + 7x * (1 + 2x)) = 4x (-1 + -2x + (1 * 7x + 2x * 7x)) = 4x (-1 + -2x + (7x + 14x2)) = 4x Combine like terms: -2x + 7x = 5x (-1 + 5x + 14x2) = 4x Solving -1 + 5x + 14x2 = 4x Solving for variable 'x'. Reorder the terms: -1 + 5x + -4x + 14x2 = 4x + -4x Combine like terms: 5x + -4x = 1x -1 + 1x + 14x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -1 + 1x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.07142857143 + 0.07142857143x + x2 = 0 Move the constant term to the right: Add '0.07142857143' to each side of the equation. -0.07142857143 + 0.07142857143x + 0.07142857143 + x2 = 0 + 0.07142857143 Reorder the terms: -0.07142857143 + 0.07142857143 + 0.07142857143x + x2 = 0 + 0.07142857143 Combine like terms: -0.07142857143 + 0.07142857143 = 0.00000000000 0.00000000000 + 0.07142857143x + x2 = 0 + 0.07142857143 0.07142857143x + x2 = 0 + 0.07142857143 Combine like terms: 0 + 0.07142857143 = 0.07142857143 0.07142857143x + x2 = 0.07142857143 The x term is 0.07142857143x. Take half its coefficient (0.03571428572). Square it (0.001275510204) and add it to both sides. Add '0.001275510204' to each side of the equation. 0.07142857143x + 0.001275510204 + x2 = 0.07142857143 + 0.001275510204 Reorder the terms: 0.001275510204 + 0.07142857143x + x2 = 0.07142857143 + 0.001275510204 Combine like terms: 0.07142857143 + 0.001275510204 = 0.072704081634 0.001275510204 + 0.07142857143x + x2 = 0.072704081634 Factor a perfect square on the left side: (x + 0.03571428572)(x + 0.03571428572) = 0.072704081634 Calculate the square root of the right side: 0.269636944 Break this problem into two subproblems by setting (x + 0.03571428572) equal to 0.269636944 and -0.269636944.Subproblem 1
x + 0.03571428572 = 0.269636944 Simplifying x + 0.03571428572 = 0.269636944 Reorder the terms: 0.03571428572 + x = 0.269636944 Solving 0.03571428572 + x = 0.269636944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03571428572' to each side of the equation. 0.03571428572 + -0.03571428572 + x = 0.269636944 + -0.03571428572 Combine like terms: 0.03571428572 + -0.03571428572 = 0.00000000000 0.00000000000 + x = 0.269636944 + -0.03571428572 x = 0.269636944 + -0.03571428572 Combine like terms: 0.269636944 + -0.03571428572 = 0.23392265828 x = 0.23392265828 Simplifying x = 0.23392265828Subproblem 2
x + 0.03571428572 = -0.269636944 Simplifying x + 0.03571428572 = -0.269636944 Reorder the terms: 0.03571428572 + x = -0.269636944 Solving 0.03571428572 + x = -0.269636944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03571428572' to each side of the equation. 0.03571428572 + -0.03571428572 + x = -0.269636944 + -0.03571428572 Combine like terms: 0.03571428572 + -0.03571428572 = 0.00000000000 0.00000000000 + x = -0.269636944 + -0.03571428572 x = -0.269636944 + -0.03571428572 Combine like terms: -0.269636944 + -0.03571428572 = -0.30535122972 x = -0.30535122972 Simplifying x = -0.30535122972Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.23392265828, -0.30535122972}
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