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Simplifying 7x + 1 = 4x2 + -40x + 100 Reorder the terms: 1 + 7x = 4x2 + -40x + 100 Reorder the terms: 1 + 7x = 100 + -40x + 4x2 Solving 1 + 7x = 100 + -40x + 4x2 Solving for variable 'x'. Reorder the terms: 1 + -100 + 7x + 40x + -4x2 = 100 + -40x + 4x2 + -100 + 40x + -4x2 Combine like terms: 1 + -100 = -99 -99 + 7x + 40x + -4x2 = 100 + -40x + 4x2 + -100 + 40x + -4x2 Combine like terms: 7x + 40x = 47x -99 + 47x + -4x2 = 100 + -40x + 4x2 + -100 + 40x + -4x2 Reorder the terms: -99 + 47x + -4x2 = 100 + -100 + -40x + 40x + 4x2 + -4x2 Combine like terms: 100 + -100 = 0 -99 + 47x + -4x2 = 0 + -40x + 40x + 4x2 + -4x2 -99 + 47x + -4x2 = -40x + 40x + 4x2 + -4x2 Combine like terms: -40x + 40x = 0 -99 + 47x + -4x2 = 0 + 4x2 + -4x2 -99 + 47x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -99 + 47x + -4x2 = 0 Factor a trinomial. (-9 + x)(11 + -4x) = 0Subproblem 1
Set the factor '(-9 + x)' equal to zero and attempt to solve: Simplifying -9 + x = 0 Solving -9 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + x = 0 + 9 x = 0 + 9 Combine like terms: 0 + 9 = 9 x = 9 Simplifying x = 9Subproblem 2
Set the factor '(11 + -4x)' equal to zero and attempt to solve: Simplifying 11 + -4x = 0 Solving 11 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -4x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -4x = 0 + -11 -4x = 0 + -11 Combine like terms: 0 + -11 = -11 -4x = -11 Divide each side by '-4'. x = 2.75 Simplifying x = 2.75Solution
x = {9, 2.75}
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