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Simplifying 6x2 + 10x = 100 Reorder the terms: 10x + 6x2 = 100 Solving 10x + 6x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 10x + 6x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 10x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + 5x + 3x2) = 0 Factor a trinomial. 2((-5 + -1x)(10 + -3x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 2
Set the factor '(10 + -3x)' equal to zero and attempt to solve: Simplifying 10 + -3x = 0 Solving 10 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -3x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3x = 0 + -10 -3x = 0 + -10 Combine like terms: 0 + -10 = -10 -3x = -10 Divide each side by '-3'. x = 3.333333333 Simplifying x = 3.333333333Solution
x = {-5, 3.333333333}
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