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Simplifying 33x2 + -50x = 32x2 + 2x + 53 Reorder the terms: -50x + 33x2 = 32x2 + 2x + 53 Reorder the terms: -50x + 33x2 = 53 + 2x + 32x2 Solving -50x + 33x2 = 53 + 2x + 32x2 Solving for variable 'x'. Reorder the terms: -53 + -50x + -2x + 33x2 + -32x2 = 53 + 2x + 32x2 + -53 + -2x + -32x2 Combine like terms: -50x + -2x = -52x -53 + -52x + 33x2 + -32x2 = 53 + 2x + 32x2 + -53 + -2x + -32x2 Combine like terms: 33x2 + -32x2 = 1x2 -53 + -52x + 1x2 = 53 + 2x + 32x2 + -53 + -2x + -32x2 Reorder the terms: -53 + -52x + 1x2 = 53 + -53 + 2x + -2x + 32x2 + -32x2 Combine like terms: 53 + -53 = 0 -53 + -52x + 1x2 = 0 + 2x + -2x + 32x2 + -32x2 -53 + -52x + 1x2 = 2x + -2x + 32x2 + -32x2 Combine like terms: 2x + -2x = 0 -53 + -52x + 1x2 = 0 + 32x2 + -32x2 -53 + -52x + 1x2 = 32x2 + -32x2 Combine like terms: 32x2 + -32x2 = 0 -53 + -52x + 1x2 = 0 Factor a trinomial. (-1 + -1x)(53 + -1x) = 0Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 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 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 2
Set the factor '(53 + -1x)' equal to zero and attempt to solve: Simplifying 53 + -1x = 0 Solving 53 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-53' to each side of the equation. 53 + -53 + -1x = 0 + -53 Combine like terms: 53 + -53 = 0 0 + -1x = 0 + -53 -1x = 0 + -53 Combine like terms: 0 + -53 = -53 -1x = -53 Divide each side by '-1'. x = 53 Simplifying x = 53Solution
x = {-1, 53}
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