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Simplifying 4135 = -10x2 + 275x + 2700 Reorder the terms: 4135 = 2700 + 275x + -10x2 Solving 4135 = 2700 + 275x + -10x2 Solving for variable 'x'. Combine like terms: 4135 + -2700 = 1435 1435 + -275x + 10x2 = 2700 + 275x + -10x2 + -2700 + -275x + 10x2 Reorder the terms: 1435 + -275x + 10x2 = 2700 + -2700 + 275x + -275x + -10x2 + 10x2 Combine like terms: 2700 + -2700 = 0 1435 + -275x + 10x2 = 0 + 275x + -275x + -10x2 + 10x2 1435 + -275x + 10x2 = 275x + -275x + -10x2 + 10x2 Combine like terms: 275x + -275x = 0 1435 + -275x + 10x2 = 0 + -10x2 + 10x2 1435 + -275x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 1435 + -275x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(287 + -55x + 2x2) = 0 Factor a trinomial. 5((7 + -1x)(41 + -2x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Subproblem 2
Set the factor '(41 + -2x)' equal to zero and attempt to solve: Simplifying 41 + -2x = 0 Solving 41 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-41' to each side of the equation. 41 + -41 + -2x = 0 + -41 Combine like terms: 41 + -41 = 0 0 + -2x = 0 + -41 -2x = 0 + -41 Combine like terms: 0 + -41 = -41 -2x = -41 Divide each side by '-2'. x = 20.5 Simplifying x = 20.5Solution
x = {7, 20.5}
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