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Simplifying -100x2 + 55x + 3 = 50x2 + -55 + 23 Reorder the terms: 3 + 55x + -100x2 = 50x2 + -55 + 23 Reorder the terms: 3 + 55x + -100x2 = -55 + 23 + 50x2 Combine like terms: -55 + 23 = -32 3 + 55x + -100x2 = -32 + 50x2 Solving 3 + 55x + -100x2 = -32 + 50x2 Solving for variable 'x'. Reorder the terms: 3 + 32 + 55x + -100x2 + -50x2 = -32 + 50x2 + 32 + -50x2 Combine like terms: 3 + 32 = 35 35 + 55x + -100x2 + -50x2 = -32 + 50x2 + 32 + -50x2 Combine like terms: -100x2 + -50x2 = -150x2 35 + 55x + -150x2 = -32 + 50x2 + 32 + -50x2 Reorder the terms: 35 + 55x + -150x2 = -32 + 32 + 50x2 + -50x2 Combine like terms: -32 + 32 = 0 35 + 55x + -150x2 = 0 + 50x2 + -50x2 35 + 55x + -150x2 = 50x2 + -50x2 Combine like terms: 50x2 + -50x2 = 0 35 + 55x + -150x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(7 + 11x + -30x2) = 0 Factor a trinomial. 5((7 + -10x)(1 + 3x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(7 + -10x)' equal to zero and attempt to solve: Simplifying 7 + -10x = 0 Solving 7 + -10x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -10x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -10x = 0 + -7 -10x = 0 + -7 Combine like terms: 0 + -7 = -7 -10x = -7 Divide each side by '-10'. x = 0.7 Simplifying x = 0.7Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {0.7, -0.3333333333}
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