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Simplifying [40000 + 2500x][16 + -1x] + [40000 + 2500x][4.00] = 0 Multiply [40000 + 2500x] * [16 + -1x] [40000[16 + -1x] + 2500x * [16 + -1x]] + [40000 + 2500x][4.00] = 0 [[16 * 40000 + -1x * 40000] + 2500x * [16 + -1x]] + [40000 + 2500x][4.00] = 0 [[640000 + -40000x] + 2500x * [16 + -1x]] + [40000 + 2500x][4.00] = 0 [640000 + -40000x + [16 * 2500x + -1x * 2500x]] + [40000 + 2500x][4.00] = 0 [640000 + -40000x + [40000x + -2500x2]] + [40000 + 2500x][4.00] = 0 Combine like terms: -40000x + 40000x = 0 [640000 + 0 + -2500x2] + [40000 + 2500x][4.00] = 0 [640000 + -2500x2] + [40000 + 2500x][4.00] = 0 Reorder the terms for easier multiplication: 640000 + -2500x2 + 4.00[40000 + 2500x] = 0 640000 + -2500x2 + [40000 * 4.00 + 2500x * 4.00] = 0 640000 + -2500x2 + [160000 + 10000x] = 0 Reorder the terms: 640000 + 160000 + 10000x + -2500x2 = 0 Combine like terms: 640000 + 160000 = 800000 800000 + 10000x + -2500x2 = 0 Solving 800000 + 10000x + -2500x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2500'. 2500(320 + 4x + -1x2) = 0 Factor a trinomial. 2500((20 + -1x)(16 + x)) = 0 Ignore the factor 2500.Subproblem 1
Set the factor '(20 + -1x)' equal to zero and attempt to solve: Simplifying 20 + -1x = 0 Solving 20 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1x = 0 + -20 -1x = 0 + -20 Combine like terms: 0 + -20 = -20 -1x = -20 Divide each side by '-1'. x = 20 Simplifying x = 20Subproblem 2
Set the factor '(16 + x)' equal to zero and attempt to solve: Simplifying 16 + x = 0 Solving 16 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 0 + -16 Combine like terms: 16 + -16 = 0 0 + x = 0 + -16 x = 0 + -16 Combine like terms: 0 + -16 = -16 x = -16 Simplifying x = -16Solution
x = {20, -16}
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