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Simplifying [40000 + 5000x][28 + -1x] + [40000 + 5000x][2.00] = 0 Multiply [40000 + 5000x] * [28 + -1x] [40000[28 + -1x] + 5000x * [28 + -1x]] + [40000 + 5000x][2.00] = 0 [[28 * 40000 + -1x * 40000] + 5000x * [28 + -1x]] + [40000 + 5000x][2.00] = 0 [[1120000 + -40000x] + 5000x * [28 + -1x]] + [40000 + 5000x][2.00] = 0 [1120000 + -40000x + [28 * 5000x + -1x * 5000x]] + [40000 + 5000x][2.00] = 0 [1120000 + -40000x + [140000x + -5000x2]] + [40000 + 5000x][2.00] = 0 Combine like terms: -40000x + 140000x = 100000x [1120000 + 100000x + -5000x2] + [40000 + 5000x][2.00] = 0 Reorder the terms for easier multiplication: 1120000 + 100000x + -5000x2 + 2.00[40000 + 5000x] = 0 1120000 + 100000x + -5000x2 + [40000 * 2.00 + 5000x * 2.00] = 0 1120000 + 100000x + -5000x2 + [80000 + 10000x] = 0 Reorder the terms: 1120000 + 80000 + 100000x + 10000x + -5000x2 = 0 Combine like terms: 1120000 + 80000 = 1200000 1200000 + 100000x + 10000x + -5000x2 = 0 Combine like terms: 100000x + 10000x = 110000x 1200000 + 110000x + -5000x2 = 0 Solving 1200000 + 110000x + -5000x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5000'. 5000(240 + 22x + -1x2) = 0 Factor a trinomial. 5000((30 + -1x)(8 + x)) = 0 Ignore the factor 5000.Subproblem 1
Set the factor '(30 + -1x)' equal to zero and attempt to solve: Simplifying 30 + -1x = 0 Solving 30 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + -1x = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -1x = 0 + -30 -1x = 0 + -30 Combine like terms: 0 + -30 = -30 -1x = -30 Divide each side by '-1'. x = 30 Simplifying x = 30Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8Solution
x = {30, -8}
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