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Simplifying 7x(x + -1) = (2x + 1)(x + -1) Reorder the terms: 7x(-1 + x) = (2x + 1)(x + -1) (-1 * 7x + x * 7x) = (2x + 1)(x + -1) (-7x + 7x2) = (2x + 1)(x + -1) Reorder the terms: -7x + 7x2 = (1 + 2x)(x + -1) Reorder the terms: -7x + 7x2 = (1 + 2x)(-1 + x) Multiply (1 + 2x) * (-1 + x) -7x + 7x2 = (1(-1 + x) + 2x * (-1 + x)) -7x + 7x2 = ((-1 * 1 + x * 1) + 2x * (-1 + x)) -7x + 7x2 = ((-1 + 1x) + 2x * (-1 + x)) -7x + 7x2 = (-1 + 1x + (-1 * 2x + x * 2x)) -7x + 7x2 = (-1 + 1x + (-2x + 2x2)) Combine like terms: 1x + -2x = -1x -7x + 7x2 = (-1 + -1x + 2x2) Solving -7x + 7x2 = -1 + -1x + 2x2 Solving for variable 'x'. Reorder the terms: 1 + -7x + x + 7x2 + -2x2 = -1 + -1x + 2x2 + 1 + x + -2x2 Combine like terms: -7x + x = -6x 1 + -6x + 7x2 + -2x2 = -1 + -1x + 2x2 + 1 + x + -2x2 Combine like terms: 7x2 + -2x2 = 5x2 1 + -6x + 5x2 = -1 + -1x + 2x2 + 1 + x + -2x2 Reorder the terms: 1 + -6x + 5x2 = -1 + 1 + -1x + x + 2x2 + -2x2 Combine like terms: -1 + 1 = 0 1 + -6x + 5x2 = 0 + -1x + x + 2x2 + -2x2 1 + -6x + 5x2 = -1x + x + 2x2 + -2x2 Combine like terms: -1x + x = 0 1 + -6x + 5x2 = 0 + 2x2 + -2x2 1 + -6x + 5x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 1 + -6x + 5x2 = 0 Factor a trinomial. (1 + -5x)(1 + -1x) = 0Subproblem 1
Set the factor '(1 + -5x)' equal to zero and attempt to solve: Simplifying 1 + -5x = 0 Solving 1 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5x = 0 + -1 -5x = 0 + -1 Combine like terms: 0 + -1 = -1 -5x = -1 Divide each side by '-5'. x = 0.2 Simplifying x = 0.2Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {0.2, 1}
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