17500=x(600-5x)

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Solution for 17500=x(600-5x) equation:


Simplifying
17500 = x(600 + -5x)
17500 = (600 * x + -5x * x)
17500 = (600x + -5x2)

Solving
17500 = 600x + -5x2

Solving for variable 'x'.

Reorder the terms:
17500 + -600x + 5x2 = 600x + -600x + -5x2 + 5x2

Combine like terms: 600x + -600x = 0
17500 + -600x + 5x2 = 0 + -5x2 + 5x2
17500 + -600x + 5x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
17500 + -600x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(3500 + -120x + x2) = 0

Factor a trinomial.
5((50 + -1x)(70 + -1x)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(50 + -1x)' equal to zero and attempt to solve: Simplifying 50 + -1x = 0 Solving 50 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + -1x = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -1x = 0 + -50 -1x = 0 + -50 Combine like terms: 0 + -50 = -50 -1x = -50 Divide each side by '-1'. x = 50 Simplifying x = 50

Subproblem 2

Set the factor '(70 + -1x)' equal to zero and attempt to solve: Simplifying 70 + -1x = 0 Solving 70 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-70' to each side of the equation. 70 + -70 + -1x = 0 + -70 Combine like terms: 70 + -70 = 0 0 + -1x = 0 + -70 -1x = 0 + -70 Combine like terms: 0 + -70 = -70 -1x = -70 Divide each side by '-1'. x = 70 Simplifying x = 70

Solution

x = {50, 70}

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