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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 = -9x (1 + -9x + 14x2) = 4x Solving 1 + -9x + 14x2 = 4x Solving for variable 'x'. Reorder the terms: 1 + -9x + -4x + 14x2 = 4x + -4x Combine like terms: -9x + -4x = -13x 1 + -13x + 14x2 = 4x + -4x Combine like terms: 4x + -4x = 0 1 + -13x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 0.07142857143 + -0.9285714286x + x2 = 0 Move the constant term to the right: Add '-0.07142857143' to each side of the equation. 0.07142857143 + -0.9285714286x + -0.07142857143 + x2 = 0 + -0.07142857143 Reorder the terms: 0.07142857143 + -0.07142857143 + -0.9285714286x + x2 = 0 + -0.07142857143 Combine like terms: 0.07142857143 + -0.07142857143 = 0.00000000000 0.00000000000 + -0.9285714286x + x2 = 0 + -0.07142857143 -0.9285714286x + x2 = 0 + -0.07142857143 Combine like terms: 0 + -0.07142857143 = -0.07142857143 -0.9285714286x + x2 = -0.07142857143 The x term is -0.9285714286x. Take half its coefficient (-0.4642857143). Square it (0.2155612245) and add it to both sides. Add '0.2155612245' to each side of the equation. -0.9285714286x + 0.2155612245 + x2 = -0.07142857143 + 0.2155612245 Reorder the terms: 0.2155612245 + -0.9285714286x + x2 = -0.07142857143 + 0.2155612245 Combine like terms: -0.07142857143 + 0.2155612245 = 0.14413265307 0.2155612245 + -0.9285714286x + x2 = 0.14413265307 Factor a perfect square on the left side: (x + -0.4642857143)(x + -0.4642857143) = 0.14413265307 Calculate the square root of the right side: 0.379648065 Break this problem into two subproblems by setting (x + -0.4642857143) equal to 0.379648065 and -0.379648065.Subproblem 1
x + -0.4642857143 = 0.379648065 Simplifying x + -0.4642857143 = 0.379648065 Reorder the terms: -0.4642857143 + x = 0.379648065 Solving -0.4642857143 + x = 0.379648065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4642857143' to each side of the equation. -0.4642857143 + 0.4642857143 + x = 0.379648065 + 0.4642857143 Combine like terms: -0.4642857143 + 0.4642857143 = 0.0000000000 0.0000000000 + x = 0.379648065 + 0.4642857143 x = 0.379648065 + 0.4642857143 Combine like terms: 0.379648065 + 0.4642857143 = 0.8439337793 x = 0.8439337793 Simplifying x = 0.8439337793Subproblem 2
x + -0.4642857143 = -0.379648065 Simplifying x + -0.4642857143 = -0.379648065 Reorder the terms: -0.4642857143 + x = -0.379648065 Solving -0.4642857143 + x = -0.379648065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4642857143' to each side of the equation. -0.4642857143 + 0.4642857143 + x = -0.379648065 + 0.4642857143 Combine like terms: -0.4642857143 + 0.4642857143 = 0.0000000000 0.0000000000 + x = -0.379648065 + 0.4642857143 x = -0.379648065 + 0.4642857143 Combine like terms: -0.379648065 + 0.4642857143 = 0.0846376493 x = 0.0846376493 Simplifying x = 0.0846376493Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8439337793, 0.0846376493}
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