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Simplifying (x + 3)(2x + -1) + -4x2 + 1 = 0 Reorder the terms: (3 + x)(2x + -1) + -4x2 + 1 = 0 Reorder the terms: (3 + x)(-1 + 2x) + -4x2 + 1 = 0 Multiply (3 + x) * (-1 + 2x) (3(-1 + 2x) + x(-1 + 2x)) + -4x2 + 1 = 0 ((-1 * 3 + 2x * 3) + x(-1 + 2x)) + -4x2 + 1 = 0 ((-3 + 6x) + x(-1 + 2x)) + -4x2 + 1 = 0 (-3 + 6x + (-1 * x + 2x * x)) + -4x2 + 1 = 0 (-3 + 6x + (-1x + 2x2)) + -4x2 + 1 = 0 Combine like terms: 6x + -1x = 5x (-3 + 5x + 2x2) + -4x2 + 1 = 0 Reorder the terms: -3 + 1 + 5x + 2x2 + -4x2 = 0 Combine like terms: -3 + 1 = -2 -2 + 5x + 2x2 + -4x2 = 0 Combine like terms: 2x2 + -4x2 = -2x2 -2 + 5x + -2x2 = 0 Solving -2 + 5x + -2x2 = 0 Solving for variable 'x'. Factor a trinomial. (-2 + x)(1 + -2x) = 0Subproblem 1
Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 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 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Subproblem 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 = {2, 0.5}
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