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Simplifying 4x2 = 30x + 100 Reorder the terms: 4x2 = 100 + 30x Solving 4x2 = 100 + 30x Solving for variable 'x'. Reorder the terms: -100 + -30x + 4x2 = 100 + 30x + -100 + -30x Reorder the terms: -100 + -30x + 4x2 = 100 + -100 + 30x + -30x Combine like terms: 100 + -100 = 0 -100 + -30x + 4x2 = 0 + 30x + -30x -100 + -30x + 4x2 = 30x + -30x Combine like terms: 30x + -30x = 0 -100 + -30x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + -15x + 2x2) = 0 Factor a trinomial. 2((-5 + -2x)(10 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve: Simplifying -5 + -2x = 0 Solving -5 + -2x = 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 + -2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x = 0 + 5 -2x = 0 + 5 Combine like terms: 0 + 5 = 5 -2x = 5 Divide each side by '-2'. x = -2.5 Simplifying x = -2.5Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 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 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solution
x = {-2.5, 10}
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