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Simplifying 33d2 + -50d = 32d2 + 2d + 53 Reorder the terms: -50d + 33d2 = 32d2 + 2d + 53 Reorder the terms: -50d + 33d2 = 53 + 2d + 32d2 Solving -50d + 33d2 = 53 + 2d + 32d2 Solving for variable 'd'. Reorder the terms: -53 + -50d + -2d + 33d2 + -32d2 = 53 + 2d + 32d2 + -53 + -2d + -32d2 Combine like terms: -50d + -2d = -52d -53 + -52d + 33d2 + -32d2 = 53 + 2d + 32d2 + -53 + -2d + -32d2 Combine like terms: 33d2 + -32d2 = 1d2 -53 + -52d + 1d2 = 53 + 2d + 32d2 + -53 + -2d + -32d2 Reorder the terms: -53 + -52d + 1d2 = 53 + -53 + 2d + -2d + 32d2 + -32d2 Combine like terms: 53 + -53 = 0 -53 + -52d + 1d2 = 0 + 2d + -2d + 32d2 + -32d2 -53 + -52d + 1d2 = 2d + -2d + 32d2 + -32d2 Combine like terms: 2d + -2d = 0 -53 + -52d + 1d2 = 0 + 32d2 + -32d2 -53 + -52d + 1d2 = 32d2 + -32d2 Combine like terms: 32d2 + -32d2 = 0 -53 + -52d + 1d2 = 0 Factor a trinomial. (-1 + -1d)(53 + -1d) = 0Subproblem 1
Set the factor '(-1 + -1d)' equal to zero and attempt to solve: Simplifying -1 + -1d = 0 Solving -1 + -1d = 0 Move all terms containing d to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1d = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1d = 0 + 1 -1d = 0 + 1 Combine like terms: 0 + 1 = 1 -1d = 1 Divide each side by '-1'. d = -1 Simplifying d = -1Subproblem 2
Set the factor '(53 + -1d)' equal to zero and attempt to solve: Simplifying 53 + -1d = 0 Solving 53 + -1d = 0 Move all terms containing d to the left, all other terms to the right. Add '-53' to each side of the equation. 53 + -53 + -1d = 0 + -53 Combine like terms: 53 + -53 = 0 0 + -1d = 0 + -53 -1d = 0 + -53 Combine like terms: 0 + -53 = -53 -1d = -53 Divide each side by '-1'. d = 53 Simplifying d = 53Solution
d = {-1, 53}
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