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Simplifying 5 + 2(x + -3) = 2[5 + -4x(x + 2)] Reorder the terms: 5 + 2(-3 + x) = 2[5 + -4x(x + 2)] 5 + (-3 * 2 + x * 2) = 2[5 + -4x(x + 2)] 5 + (-6 + 2x) = 2[5 + -4x(x + 2)] Combine like terms: 5 + -6 = -1 -1 + 2x = 2[5 + -4x(x + 2)] Reorder the terms: -1 + 2x = 2[5 + -4x(2 + x)] -1 + 2x = 2[5 + (2 * -4x + x * -4x)] -1 + 2x = 2[5 + (-8x + -4x2)] -1 + 2x = [5 * 2 + -8x * 2 + -4x2 * 2] -1 + 2x = [10 + -16x + -8x2] Solving -1 + 2x = 10 + -16x + -8x2 Solving for variable 'x'. Reorder the terms: -1 + -10 + 2x + 16x + 8x2 = 10 + -16x + -8x2 + -10 + 16x + 8x2 Combine like terms: -1 + -10 = -11 -11 + 2x + 16x + 8x2 = 10 + -16x + -8x2 + -10 + 16x + 8x2 Combine like terms: 2x + 16x = 18x -11 + 18x + 8x2 = 10 + -16x + -8x2 + -10 + 16x + 8x2 Reorder the terms: -11 + 18x + 8x2 = 10 + -10 + -16x + 16x + -8x2 + 8x2 Combine like terms: 10 + -10 = 0 -11 + 18x + 8x2 = 0 + -16x + 16x + -8x2 + 8x2 -11 + 18x + 8x2 = -16x + 16x + -8x2 + 8x2 Combine like terms: -16x + 16x = 0 -11 + 18x + 8x2 = 0 + -8x2 + 8x2 -11 + 18x + 8x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 -11 + 18x + 8x2 = 0 Factor a trinomial. (-11 + -4x)(1 + -2x) = 0Subproblem 1
Set the factor '(-11 + -4x)' equal to zero and attempt to solve: Simplifying -11 + -4x = 0 Solving -11 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -4x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -4x = 0 + 11 -4x = 0 + 11 Combine like terms: 0 + 11 = 11 -4x = 11 Divide each side by '-4'. x = -2.75 Simplifying x = -2.75Subproblem 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 = {-2.75, 0.5}
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