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Simplifying 25x(x + 7) = 6500 Reorder the terms: 25x(7 + x) = 6500 (7 * 25x + x * 25x) = 6500 (175x + 25x2) = 6500 Solving 175x + 25x2 = 6500 Solving for variable 'x'. Reorder the terms: -6500 + 175x + 25x2 = 6500 + -6500 Combine like terms: 6500 + -6500 = 0 -6500 + 175x + 25x2 = 0 Factor out the Greatest Common Factor (GCF), '25'. 25(-260 + 7x + x2) = 0 Factor a trinomial. 25((-20 + -1x)(13 + -1x)) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(-20 + -1x)' equal to zero and attempt to solve: Simplifying -20 + -1x = 0 Solving -20 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + -1x = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -1x = 0 + 20 -1x = 0 + 20 Combine like terms: 0 + 20 = 20 -1x = 20 Divide each side by '-1'. x = -20 Simplifying x = -20Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve: Simplifying 13 + -1x = 0 Solving 13 + -1x = 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 + -1x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1x = 0 + -13 -1x = 0 + -13 Combine like terms: 0 + -13 = -13 -1x = -13 Divide each side by '-1'. x = 13 Simplifying x = 13Solution
x = {-20, 13}
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