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Simplifying [40000 + 2500x][28 + -1x] + [40000 + 2500x][4.00] = 0 Multiply [40000 + 2500x] * [28 + -1x] [40000[28 + -1x] + 2500x * [28 + -1x]] + [40000 + 2500x][4.00] = 0 [[28 * 40000 + -1x * 40000] + 2500x * [28 + -1x]] + [40000 + 2500x][4.00] = 0 [[1120000 + -40000x] + 2500x * [28 + -1x]] + [40000 + 2500x][4.00] = 0 [1120000 + -40000x + [28 * 2500x + -1x * 2500x]] + [40000 + 2500x][4.00] = 0 [1120000 + -40000x + [70000x + -2500x2]] + [40000 + 2500x][4.00] = 0 Combine like terms: -40000x + 70000x = 30000x [1120000 + 30000x + -2500x2] + [40000 + 2500x][4.00] = 0 Reorder the terms for easier multiplication: 1120000 + 30000x + -2500x2 + 4.00[40000 + 2500x] = 0 1120000 + 30000x + -2500x2 + [40000 * 4.00 + 2500x * 4.00] = 0 1120000 + 30000x + -2500x2 + [160000 + 10000x] = 0 Reorder the terms: 1120000 + 160000 + 30000x + 10000x + -2500x2 = 0 Combine like terms: 1120000 + 160000 = 1280000 1280000 + 30000x + 10000x + -2500x2 = 0 Combine like terms: 30000x + 10000x = 40000x 1280000 + 40000x + -2500x2 = 0 Solving 1280000 + 40000x + -2500x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2500'. 2500(512 + 16x + -1x2) = 0 Factor a trinomial. 2500((32 + -1x)(16 + x)) = 0 Ignore the factor 2500.Subproblem 1
Set the factor '(32 + -1x)' equal to zero and attempt to solve: Simplifying 32 + -1x = 0 Solving 32 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + -1x = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -1x = 0 + -32 -1x = 0 + -32 Combine like terms: 0 + -32 = -32 -1x = -32 Divide each side by '-1'. x = 32 Simplifying x = 32Subproblem 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 = {32, -16}
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