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Simplifying (300 + 10x)(100 + -1x) = 0 Multiply (300 + 10x) * (100 + -1x) (300(100 + -1x) + 10x * (100 + -1x)) = 0 ((100 * 300 + -1x * 300) + 10x * (100 + -1x)) = 0 ((30000 + -300x) + 10x * (100 + -1x)) = 0 (30000 + -300x + (100 * 10x + -1x * 10x)) = 0 (30000 + -300x + (1000x + -10x2)) = 0 Combine like terms: -300x + 1000x = 700x (30000 + 700x + -10x2) = 0 Solving 30000 + 700x + -10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(3000 + 70x + -1x2) = 0 Factor a trinomial. 10((100 + -1x)(30 + x)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(100 + -1x)' equal to zero and attempt to solve: Simplifying 100 + -1x = 0 Solving 100 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + -1x = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -1x = 0 + -100 -1x = 0 + -100 Combine like terms: 0 + -100 = -100 -1x = -100 Divide each side by '-1'. x = 100 Simplifying x = 100Subproblem 2
Set the factor '(30 + x)' equal to zero and attempt to solve: Simplifying 30 + x = 0 Solving 30 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = 0 + -30 Combine like terms: 30 + -30 = 0 0 + x = 0 + -30 x = 0 + -30 Combine like terms: 0 + -30 = -30 x = -30 Simplifying x = -30Solution
x = {100, -30}
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