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Simplifying 15600 = (73 + x)(225 + -5x) Multiply (73 + x) * (225 + -5x) 15600 = (73(225 + -5x) + x(225 + -5x)) 15600 = ((225 * 73 + -5x * 73) + x(225 + -5x)) 15600 = ((16425 + -365x) + x(225 + -5x)) 15600 = (16425 + -365x + (225 * x + -5x * x)) 15600 = (16425 + -365x + (225x + -5x2)) Combine like terms: -365x + 225x = -140x 15600 = (16425 + -140x + -5x2) Solving 15600 = 16425 + -140x + -5x2 Solving for variable 'x'. Combine like terms: 15600 + -16425 = -825 -825 + 140x + 5x2 = 16425 + -140x + -5x2 + -16425 + 140x + 5x2 Reorder the terms: -825 + 140x + 5x2 = 16425 + -16425 + -140x + 140x + -5x2 + 5x2 Combine like terms: 16425 + -16425 = 0 -825 + 140x + 5x2 = 0 + -140x + 140x + -5x2 + 5x2 -825 + 140x + 5x2 = -140x + 140x + -5x2 + 5x2 Combine like terms: -140x + 140x = 0 -825 + 140x + 5x2 = 0 + -5x2 + 5x2 -825 + 140x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -825 + 140x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-165 + 28x + x2) = 0 Factor a trinomial. 5((-33 + -1x)(5 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-33 + -1x)' equal to zero and attempt to solve: Simplifying -33 + -1x = 0 Solving -33 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '33' to each side of the equation. -33 + 33 + -1x = 0 + 33 Combine like terms: -33 + 33 = 0 0 + -1x = 0 + 33 -1x = 0 + 33 Combine like terms: 0 + 33 = 33 -1x = 33 Divide each side by '-1'. x = -33 Simplifying x = -33Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-33, 5}
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