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Simplifying 0 = 400 + -80x + 3x2 Solving 0 = 400 + -80x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -400 = -400 -400 + 80x + -3x2 = 400 + -80x + 3x2 + -400 + 80x + -3x2 Reorder the terms: -400 + 80x + -3x2 = 400 + -400 + -80x + 80x + 3x2 + -3x2 Combine like terms: 400 + -400 = 0 -400 + 80x + -3x2 = 0 + -80x + 80x + 3x2 + -3x2 -400 + 80x + -3x2 = -80x + 80x + 3x2 + -3x2 Combine like terms: -80x + 80x = 0 -400 + 80x + -3x2 = 0 + 3x2 + -3x2 -400 + 80x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -400 + 80x + -3x2 = 0 Factor a trinomial. (-20 + x)(20 + -3x) = 0Subproblem 1
Set the factor '(-20 + x)' equal to zero and attempt to solve: Simplifying -20 + x = 0 Solving -20 + x = 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 + x = 0 + 20 Combine like terms: -20 + 20 = 0 0 + x = 0 + 20 x = 0 + 20 Combine like terms: 0 + 20 = 20 x = 20 Simplifying x = 20Subproblem 2
Set the factor '(20 + -3x)' equal to zero and attempt to solve: Simplifying 20 + -3x = 0 Solving 20 + -3x = 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 + -3x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -3x = 0 + -20 -3x = 0 + -20 Combine like terms: 0 + -20 = -20 -3x = -20 Divide each side by '-3'. x = 6.666666667 Simplifying x = 6.666666667Solution
x = {20, 6.666666667}
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