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Simplifying 50x2 + 105x + 55 = 78 Reorder the terms: 55 + 105x + 50x2 = 78 Solving 55 + 105x + 50x2 = 78 Solving for variable 'x'. Reorder the terms: 55 + -78 + 105x + 50x2 = 78 + -78 Combine like terms: 55 + -78 = -23 -23 + 105x + 50x2 = 78 + -78 Combine like terms: 78 + -78 = 0 -23 + 105x + 50x2 = 0 Factor a trinomial. (-23 + -10x)(1 + -5x) = 0Subproblem 1
Set the factor '(-23 + -10x)' equal to zero and attempt to solve: Simplifying -23 + -10x = 0 Solving -23 + -10x = 0 Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + -10x = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -10x = 0 + 23 -10x = 0 + 23 Combine like terms: 0 + 23 = 23 -10x = 23 Divide each side by '-10'. x = -2.3 Simplifying x = -2.3Subproblem 2
Set the factor '(1 + -5x)' equal to zero and attempt to solve: Simplifying 1 + -5x = 0 Solving 1 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5x = 0 + -1 -5x = 0 + -1 Combine like terms: 0 + -1 = -1 -5x = -1 Divide each side by '-5'. x = 0.2 Simplifying x = 0.2Solution
x = {-2.3, 0.2}
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