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Simplifying 0.5x(x + -3) = (x + -3)(1.5x + -1) Reorder the terms: 0.5x(-3 + x) = (x + -3)(1.5x + -1) (-3 * 0.5x + x * 0.5x) = (x + -3)(1.5x + -1) (-1.5x + 0.5x2) = (x + -3)(1.5x + -1) Reorder the terms: -1.5x + 0.5x2 = (-3 + x)(1.5x + -1) Reorder the terms: -1.5x + 0.5x2 = (-3 + x)(-1 + 1.5x) Multiply (-3 + x) * (-1 + 1.5x) -1.5x + 0.5x2 = (-3(-1 + 1.5x) + x(-1 + 1.5x)) -1.5x + 0.5x2 = ((-1 * -3 + 1.5x * -3) + x(-1 + 1.5x)) -1.5x + 0.5x2 = ((3 + -4.5x) + x(-1 + 1.5x)) -1.5x + 0.5x2 = (3 + -4.5x + (-1 * x + 1.5x * x)) -1.5x + 0.5x2 = (3 + -4.5x + (-1x + 1.5x2)) Combine like terms: -4.5x + -1x = -5.5x -1.5x + 0.5x2 = (3 + -5.5x + 1.5x2) Solving -1.5x + 0.5x2 = 3 + -5.5x + 1.5x2 Solving for variable 'x'. Reorder the terms: -3 + -1.5x + 5.5x + 0.5x2 + -1.5x2 = 3 + -5.5x + 1.5x2 + -3 + 5.5x + -1.5x2 Combine like terms: -1.5x + 5.5x = 4x -3 + 4x + 0.5x2 + -1.5x2 = 3 + -5.5x + 1.5x2 + -3 + 5.5x + -1.5x2 Combine like terms: 0.5x2 + -1.5x2 = -1x2 -3 + 4x + -1x2 = 3 + -5.5x + 1.5x2 + -3 + 5.5x + -1.5x2 Reorder the terms: -3 + 4x + -1x2 = 3 + -3 + -5.5x + 5.5x + 1.5x2 + -1.5x2 Combine like terms: 3 + -3 = 0 -3 + 4x + -1x2 = 0 + -5.5x + 5.5x + 1.5x2 + -1.5x2 -3 + 4x + -1x2 = -5.5x + 5.5x + 1.5x2 + -1.5x2 Combine like terms: -5.5x + 5.5x = 0.0 -3 + 4x + -1x2 = 0.0 + 1.5x2 + -1.5x2 -3 + 4x + -1x2 = 1.5x2 + -1.5x2 Combine like terms: 1.5x2 + -1.5x2 = 0.0 -3 + 4x + -1x2 = 0.0 Factor a trinomial. (-3 + x)(1 + -1x) = 0.0Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3Subproblem 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 = {3, 1}
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