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Simplifying (2x + 1)(x + -2) + 1 = x(x + 1) + -5 Reorder the terms: (1 + 2x)(x + -2) + 1 = x(x + 1) + -5 Reorder the terms: (1 + 2x)(-2 + x) + 1 = x(x + 1) + -5 Multiply (1 + 2x) * (-2 + x) (1(-2 + x) + 2x * (-2 + x)) + 1 = x(x + 1) + -5 ((-2 * 1 + x * 1) + 2x * (-2 + x)) + 1 = x(x + 1) + -5 ((-2 + 1x) + 2x * (-2 + x)) + 1 = x(x + 1) + -5 (-2 + 1x + (-2 * 2x + x * 2x)) + 1 = x(x + 1) + -5 (-2 + 1x + (-4x + 2x2)) + 1 = x(x + 1) + -5 Combine like terms: 1x + -4x = -3x (-2 + -3x + 2x2) + 1 = x(x + 1) + -5 Reorder the terms: -2 + 1 + -3x + 2x2 = x(x + 1) + -5 Combine like terms: -2 + 1 = -1 -1 + -3x + 2x2 = x(x + 1) + -5 Reorder the terms: -1 + -3x + 2x2 = x(1 + x) + -5 -1 + -3x + 2x2 = (1 * x + x * x) + -5 -1 + -3x + 2x2 = (1x + x2) + -5 Reorder the terms: -1 + -3x + 2x2 = -5 + 1x + x2 Solving -1 + -3x + 2x2 = -5 + 1x + x2 Solving for variable 'x'. Reorder the terms: -1 + 5 + -3x + -1x + 2x2 + -1x2 = -5 + 1x + x2 + 5 + -1x + -1x2 Combine like terms: -1 + 5 = 4 4 + -3x + -1x + 2x2 + -1x2 = -5 + 1x + x2 + 5 + -1x + -1x2 Combine like terms: -3x + -1x = -4x 4 + -4x + 2x2 + -1x2 = -5 + 1x + x2 + 5 + -1x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 4 + -4x + 1x2 = -5 + 1x + x2 + 5 + -1x + -1x2 Reorder the terms: 4 + -4x + 1x2 = -5 + 5 + 1x + -1x + x2 + -1x2 Combine like terms: -5 + 5 = 0 4 + -4x + 1x2 = 0 + 1x + -1x + x2 + -1x2 4 + -4x + 1x2 = 1x + -1x + x2 + -1x2 Combine like terms: 1x + -1x = 0 4 + -4x + 1x2 = 0 + x2 + -1x2 4 + -4x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 4 + -4x + 1x2 = 0 Factor a trinomial. (2 + -1x)(2 + -1x) = 0Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {2, 2}
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