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Simplifying 4(x2 + 4x + 4) + -3(x2 + -6x + 9) = x2 + 5(3x + -4x2 + -1) Reorder the terms: 4(4 + 4x + x2) + -3(x2 + -6x + 9) = x2 + 5(3x + -4x2 + -1) (4 * 4 + 4x * 4 + x2 * 4) + -3(x2 + -6x + 9) = x2 + 5(3x + -4x2 + -1) (16 + 16x + 4x2) + -3(x2 + -6x + 9) = x2 + 5(3x + -4x2 + -1) Reorder the terms: 16 + 16x + 4x2 + -3(9 + -6x + x2) = x2 + 5(3x + -4x2 + -1) 16 + 16x + 4x2 + (9 * -3 + -6x * -3 + x2 * -3) = x2 + 5(3x + -4x2 + -1) 16 + 16x + 4x2 + (-27 + 18x + -3x2) = x2 + 5(3x + -4x2 + -1) Reorder the terms: 16 + -27 + 16x + 18x + 4x2 + -3x2 = x2 + 5(3x + -4x2 + -1) Combine like terms: 16 + -27 = -11 -11 + 16x + 18x + 4x2 + -3x2 = x2 + 5(3x + -4x2 + -1) Combine like terms: 16x + 18x = 34x -11 + 34x + 4x2 + -3x2 = x2 + 5(3x + -4x2 + -1) Combine like terms: 4x2 + -3x2 = 1x2 -11 + 34x + 1x2 = x2 + 5(3x + -4x2 + -1) Reorder the terms: -11 + 34x + 1x2 = x2 + 5(-1 + 3x + -4x2) -11 + 34x + 1x2 = x2 + (-1 * 5 + 3x * 5 + -4x2 * 5) -11 + 34x + 1x2 = x2 + (-5 + 15x + -20x2) Reorder the terms: -11 + 34x + 1x2 = -5 + 15x + x2 + -20x2 Combine like terms: x2 + -20x2 = -19x2 -11 + 34x + 1x2 = -5 + 15x + -19x2 Solving -11 + 34x + 1x2 = -5 + 15x + -19x2 Solving for variable 'x'. Reorder the terms: -11 + 5 + 34x + -15x + 1x2 + 19x2 = -5 + 15x + -19x2 + 5 + -15x + 19x2 Combine like terms: -11 + 5 = -6 -6 + 34x + -15x + 1x2 + 19x2 = -5 + 15x + -19x2 + 5 + -15x + 19x2 Combine like terms: 34x + -15x = 19x -6 + 19x + 1x2 + 19x2 = -5 + 15x + -19x2 + 5 + -15x + 19x2 Combine like terms: 1x2 + 19x2 = 20x2 -6 + 19x + 20x2 = -5 + 15x + -19x2 + 5 + -15x + 19x2 Reorder the terms: -6 + 19x + 20x2 = -5 + 5 + 15x + -15x + -19x2 + 19x2 Combine like terms: -5 + 5 = 0 -6 + 19x + 20x2 = 0 + 15x + -15x + -19x2 + 19x2 -6 + 19x + 20x2 = 15x + -15x + -19x2 + 19x2 Combine like terms: 15x + -15x = 0 -6 + 19x + 20x2 = 0 + -19x2 + 19x2 -6 + 19x + 20x2 = -19x2 + 19x2 Combine like terms: -19x2 + 19x2 = 0 -6 + 19x + 20x2 = 0 Factor a trinomial. (-6 + -5x)(1 + -4x) = 0Subproblem 1
Set the factor '(-6 + -5x)' equal to zero and attempt to solve: Simplifying -6 + -5x = 0 Solving -6 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -5x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -5x = 0 + 6 -5x = 0 + 6 Combine like terms: 0 + 6 = 6 -5x = 6 Divide each side by '-5'. x = -1.2 Simplifying x = -1.2Subproblem 2
Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25Solution
x = {-1.2, 0.25}
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