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Simplifying 9x2 + 24x + 16 + -1(36 + 25x2 + -20x + 4) = 0 Reorder the terms: 9x2 + 24x + 16 + -1(36 + 4 + -20x + 25x2) = 0 Combine like terms: 36 + 4 = 40 9x2 + 24x + 16 + -1(40 + -20x + 25x2) = 0 9x2 + 24x + 16 + (40 * -1 + -20x * -1 + 25x2 * -1) = 0 9x2 + 24x + 16 + (-40 + 20x + -25x2) = 0 Reorder the terms: 16 + -40 + 24x + 20x + 9x2 + -25x2 = 0 Combine like terms: 16 + -40 = -24 -24 + 24x + 20x + 9x2 + -25x2 = 0 Combine like terms: 24x + 20x = 44x -24 + 44x + 9x2 + -25x2 = 0 Combine like terms: 9x2 + -25x2 = -16x2 -24 + 44x + -16x2 = 0 Solving -24 + 44x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-6 + 11x + -4x2) = 0 Factor a trinomial. 4((-2 + x)(3 + -4x)) = 0 Ignore the factor 4.Subproblem 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 '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 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 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75Solution
x = {2, 0.75}
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