48400(100-x)(100-x)=32400(100+x)(100+x)

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Solution for 48400(100-x)(100-x)=32400(100+x)(100+x) equation:


Simplifying
48400(100 + -1x)(100 + -1x) = 32400(100 + x)(100 + x)

Multiply (100 + -1x) * (100 + -1x)
48400(100(100 + -1x) + -1x * (100 + -1x)) = 32400(100 + x)(100 + x)
48400((100 * 100 + -1x * 100) + -1x * (100 + -1x)) = 32400(100 + x)(100 + x)
48400((10000 + -100x) + -1x * (100 + -1x)) = 32400(100 + x)(100 + x)
48400(10000 + -100x + (100 * -1x + -1x * -1x)) = 32400(100 + x)(100 + x)
48400(10000 + -100x + (-100x + 1x2)) = 32400(100 + x)(100 + x)

Combine like terms: -100x + -100x = -200x
48400(10000 + -200x + 1x2) = 32400(100 + x)(100 + x)
(10000 * 48400 + -200x * 48400 + 1x2 * 48400) = 32400(100 + x)(100 + x)
(484000000 + -9680000x + 48400x2) = 32400(100 + x)(100 + x)

Multiply (100 + x) * (100 + x)
484000000 + -9680000x + 48400x2 = 32400(100(100 + x) + x(100 + x))
484000000 + -9680000x + 48400x2 = 32400((100 * 100 + x * 100) + x(100 + x))
484000000 + -9680000x + 48400x2 = 32400((10000 + 100x) + x(100 + x))
484000000 + -9680000x + 48400x2 = 32400(10000 + 100x + (100 * x + x * x))
484000000 + -9680000x + 48400x2 = 32400(10000 + 100x + (100x + x2))

Combine like terms: 100x + 100x = 200x
484000000 + -9680000x + 48400x2 = 32400(10000 + 200x + x2)
484000000 + -9680000x + 48400x2 = (10000 * 32400 + 200x * 32400 + x2 * 32400)
484000000 + -9680000x + 48400x2 = (324000000 + 6480000x + 32400x2)

Solving
484000000 + -9680000x + 48400x2 = 324000000 + 6480000x + 32400x2

Solving for variable 'x'.

Reorder the terms:
484000000 + -324000000 + -9680000x + -6480000x + 48400x2 + -32400x2 = 324000000 + 6480000x + 32400x2 + -324000000 + -6480000x + -32400x2

Combine like terms: 484000000 + -324000000 = 160000000
160000000 + -9680000x + -6480000x + 48400x2 + -32400x2 = 324000000 + 6480000x + 32400x2 + -324000000 + -6480000x + -32400x2

Combine like terms: -9680000x + -6480000x = -16160000x
160000000 + -16160000x + 48400x2 + -32400x2 = 324000000 + 6480000x + 32400x2 + -324000000 + -6480000x + -32400x2

Combine like terms: 48400x2 + -32400x2 = 16000x2
160000000 + -16160000x + 16000x2 = 324000000 + 6480000x + 32400x2 + -324000000 + -6480000x + -32400x2

Reorder the terms:
160000000 + -16160000x + 16000x2 = 324000000 + -324000000 + 6480000x + -6480000x + 32400x2 + -32400x2

Combine like terms: 324000000 + -324000000 = 0
160000000 + -16160000x + 16000x2 = 0 + 6480000x + -6480000x + 32400x2 + -32400x2
160000000 + -16160000x + 16000x2 = 6480000x + -6480000x + 32400x2 + -32400x2

Combine like terms: 6480000x + -6480000x = 0
160000000 + -16160000x + 16000x2 = 0 + 32400x2 + -32400x2
160000000 + -16160000x + 16000x2 = 32400x2 + -32400x2

Combine like terms: 32400x2 + -32400x2 = 0
160000000 + -16160000x + 16000x2 = 0

Factor out the Greatest Common Factor (GCF), '16000'.
16000(10000 + -1010x + x2) = 0

Factor a trinomial.
16000((10 + -1x)(1000 + -1x)) = 0

Ignore the factor 16000.

Subproblem 1

Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10

Subproblem 2

Set the factor '(1000 + -1x)' equal to zero and attempt to solve: Simplifying 1000 + -1x = 0 Solving 1000 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1000' to each side of the equation. 1000 + -1000 + -1x = 0 + -1000 Combine like terms: 1000 + -1000 = 0 0 + -1x = 0 + -1000 -1x = 0 + -1000 Combine like terms: 0 + -1000 = -1000 -1x = -1000 Divide each side by '-1'. x = 1000 Simplifying x = 1000

Solution

x = {10, 1000}

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