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Simplifying (225 + -5x)(75 + x) = 15795 Multiply (225 + -5x) * (75 + x) (225(75 + x) + -5x * (75 + x)) = 15795 ((75 * 225 + x * 225) + -5x * (75 + x)) = 15795 ((16875 + 225x) + -5x * (75 + x)) = 15795 (16875 + 225x + (75 * -5x + x * -5x)) = 15795 (16875 + 225x + (-375x + -5x2)) = 15795 Combine like terms: 225x + -375x = -150x (16875 + -150x + -5x2) = 15795 Solving 16875 + -150x + -5x2 = 15795 Solving for variable 'x'. Reorder the terms: 16875 + -15795 + -150x + -5x2 = 15795 + -15795 Combine like terms: 16875 + -15795 = 1080 1080 + -150x + -5x2 = 15795 + -15795 Combine like terms: 15795 + -15795 = 0 1080 + -150x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(216 + -30x + -1x2) = 0 Factor a trinomial. 5((6 + -1x)(36 + x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Subproblem 2
Set the factor '(36 + x)' equal to zero and attempt to solve: Simplifying 36 + x = 0 Solving 36 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + -36 + x = 0 + -36 Combine like terms: 36 + -36 = 0 0 + x = 0 + -36 x = 0 + -36 Combine like terms: 0 + -36 = -36 x = -36 Simplifying x = -36Solution
x = {6, -36}
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