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Simplifying 2x2 + 7x + 4 + 4x2 + 9x + 5 = 41 Reorder the terms: 4 + 5 + 7x + 9x + 2x2 + 4x2 = 41 Combine like terms: 4 + 5 = 9 9 + 7x + 9x + 2x2 + 4x2 = 41 Combine like terms: 7x + 9x = 16x 9 + 16x + 2x2 + 4x2 = 41 Combine like terms: 2x2 + 4x2 = 6x2 9 + 16x + 6x2 = 41 Solving 9 + 16x + 6x2 = 41 Solving for variable 'x'. Reorder the terms: 9 + -41 + 16x + 6x2 = 41 + -41 Combine like terms: 9 + -41 = -32 -32 + 16x + 6x2 = 41 + -41 Combine like terms: 41 + -41 = 0 -32 + 16x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + 8x + 3x2) = 0 Factor a trinomial. 2((-4 + -1x)(4 + -3x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333Solution
x = {-4, 1.333333333}
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