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Simplifying 6845 = x2 + 5x + 45 Reorder the terms: 6845 = 45 + 5x + x2 Solving 6845 = 45 + 5x + x2 Solving for variable 'x'. Combine like terms: 6845 + -45 = 6800 6800 + -5x + -1x2 = 45 + 5x + x2 + -45 + -5x + -1x2 Reorder the terms: 6800 + -5x + -1x2 = 45 + -45 + 5x + -5x + x2 + -1x2 Combine like terms: 45 + -45 = 0 6800 + -5x + -1x2 = 0 + 5x + -5x + x2 + -1x2 6800 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 6800 + -5x + -1x2 = 0 + x2 + -1x2 6800 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 6800 + -5x + -1x2 = 0 Factor a trinomial. (80 + -1x)(85 + x) = 0Subproblem 1
Set the factor '(80 + -1x)' equal to zero and attempt to solve: Simplifying 80 + -1x = 0 Solving 80 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -80 + -1x = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -1x = 0 + -80 -1x = 0 + -80 Combine like terms: 0 + -80 = -80 -1x = -80 Divide each side by '-1'. x = 80 Simplifying x = 80Subproblem 2
Set the factor '(85 + x)' equal to zero and attempt to solve: Simplifying 85 + x = 0 Solving 85 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-85' to each side of the equation. 85 + -85 + x = 0 + -85 Combine like terms: 85 + -85 = 0 0 + x = 0 + -85 x = 0 + -85 Combine like terms: 0 + -85 = -85 x = -85 Simplifying x = -85Solution
x = {80, -85}
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