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Simplifying (21 + -1x)(20 + -1x) = 210 Multiply (21 + -1x) * (20 + -1x) (21(20 + -1x) + -1x * (20 + -1x)) = 210 ((20 * 21 + -1x * 21) + -1x * (20 + -1x)) = 210 ((420 + -21x) + -1x * (20 + -1x)) = 210 (420 + -21x + (20 * -1x + -1x * -1x)) = 210 (420 + -21x + (-20x + 1x2)) = 210 Combine like terms: -21x + -20x = -41x (420 + -41x + 1x2) = 210 Solving 420 + -41x + 1x2 = 210 Solving for variable 'x'. Reorder the terms: 420 + -210 + -41x + 1x2 = 210 + -210 Combine like terms: 420 + -210 = 210 210 + -41x + 1x2 = 210 + -210 Combine like terms: 210 + -210 = 0 210 + -41x + 1x2 = 0 Factor a trinomial. (6 + -1x)(35 + -1x) = 0Subproblem 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 '(35 + -1x)' equal to zero and attempt to solve: Simplifying 35 + -1x = 0 Solving 35 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + -1x = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -1x = 0 + -35 -1x = 0 + -35 Combine like terms: 0 + -35 = -35 -1x = -35 Divide each side by '-1'. x = 35 Simplifying x = 35Solution
x = {6, 35}
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