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Simplifying 4x2 + -1 = (2x + 1)(3x + -5) Reorder the terms: -1 + 4x2 = (2x + 1)(3x + -5) Reorder the terms: -1 + 4x2 = (1 + 2x)(3x + -5) Reorder the terms: -1 + 4x2 = (1 + 2x)(-5 + 3x) Multiply (1 + 2x) * (-5 + 3x) -1 + 4x2 = (1(-5 + 3x) + 2x * (-5 + 3x)) -1 + 4x2 = ((-5 * 1 + 3x * 1) + 2x * (-5 + 3x)) -1 + 4x2 = ((-5 + 3x) + 2x * (-5 + 3x)) -1 + 4x2 = (-5 + 3x + (-5 * 2x + 3x * 2x)) -1 + 4x2 = (-5 + 3x + (-10x + 6x2)) Combine like terms: 3x + -10x = -7x -1 + 4x2 = (-5 + -7x + 6x2) Solving -1 + 4x2 = -5 + -7x + 6x2 Solving for variable 'x'. Reorder the terms: -1 + 5 + 7x + 4x2 + -6x2 = -5 + -7x + 6x2 + 5 + 7x + -6x2 Combine like terms: -1 + 5 = 4 4 + 7x + 4x2 + -6x2 = -5 + -7x + 6x2 + 5 + 7x + -6x2 Combine like terms: 4x2 + -6x2 = -2x2 4 + 7x + -2x2 = -5 + -7x + 6x2 + 5 + 7x + -6x2 Reorder the terms: 4 + 7x + -2x2 = -5 + 5 + -7x + 7x + 6x2 + -6x2 Combine like terms: -5 + 5 = 0 4 + 7x + -2x2 = 0 + -7x + 7x + 6x2 + -6x2 4 + 7x + -2x2 = -7x + 7x + 6x2 + -6x2 Combine like terms: -7x + 7x = 0 4 + 7x + -2x2 = 0 + 6x2 + -6x2 4 + 7x + -2x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 4 + 7x + -2x2 = 0 Factor a trinomial. (4 + -1x)(1 + 2x) = 0Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {4, -0.5}
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