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Simplifying 50x + 100x(x + 4) = 1300 Reorder the terms: 50x + 100x(4 + x) = 1300 50x + (4 * 100x + x * 100x) = 1300 50x + (400x + 100x2) = 1300 Combine like terms: 50x + 400x = 450x 450x + 100x2 = 1300 Solving 450x + 100x2 = 1300 Solving for variable 'x'. Reorder the terms: -1300 + 450x + 100x2 = 1300 + -1300 Combine like terms: 1300 + -1300 = 0 -1300 + 450x + 100x2 = 0 Factor out the Greatest Common Factor (GCF), '50'. 50(-26 + 9x + 2x2) = 0 Factor a trinomial. 50((-13 + -2x)(2 + -1x)) = 0 Ignore the factor 50.Subproblem 1
Set the factor '(-13 + -2x)' equal to zero and attempt to solve: Simplifying -13 + -2x = 0 Solving -13 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -2x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -2x = 0 + 13 -2x = 0 + 13 Combine like terms: 0 + 13 = 13 -2x = 13 Divide each side by '-2'. x = -6.5 Simplifying x = -6.5Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-6.5, 2}
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