9000=(30+2x)(250-25x)

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Solution for 9000=(30+2x)(250-25x) equation: 


Simplifying
9000 = (30 + 2x)(250 + -25x)

Multiply (30 + 2x) * (250 + -25x)
9000 = (30(250 + -25x) + 2x * (250 + -25x))
9000 = ((250 * 30 + -25x * 30) + 2x * (250 + -25x))
9000 = ((7500 + -750x) + 2x * (250 + -25x))
9000 = (7500 + -750x + (250 * 2x + -25x * 2x))
9000 = (7500 + -750x + (500x + -50x2))

Combine like terms: -750x + 500x = -250x
9000 = (7500 + -250x + -50x2)

Solving
9000 = 7500 + -250x + -50x2

Solving for variable 'x'.

Combine like terms: 9000 + -7500 = 1500
1500 + 250x + 50x2 = 7500 + -250x + -50x2 + -7500 + 250x + 50x2

Reorder the terms:
1500 + 250x + 50x2 = 7500 + -7500 + -250x + 250x + -50x2 + 50x2

Combine like terms: 7500 + -7500 = 0
1500 + 250x + 50x2 = 0 + -250x + 250x + -50x2 + 50x2
1500 + 250x + 50x2 = -250x + 250x + -50x2 + 50x2

Combine like terms: -250x + 250x = 0
1500 + 250x + 50x2 = 0 + -50x2 + 50x2
1500 + 250x + 50x2 = -50x2 + 50x2

Combine like terms: -50x2 + 50x2 = 0
1500 + 250x + 50x2 = 0

Factor out the Greatest Common Factor (GCF), '50'.
50(30 + 5x + x2) = 0

Ignore the factor 50.

Subproblem 1
Set the factor '(30 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
30 + 5x + x2 = 0

Solving
30 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + 5x + -30 + x2 = 0 + -30

Reorder the terms:
30 + -30 + 5x + x2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + 5x + x2 = 0 + -30
5x + x2 = 0 + -30

Combine like terms: 0 + -30 = -30
5x + x2 = -30

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -30 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -30 + 6.25

Combine like terms: -30 + 6.25 = -23.75
6.25 + 5x + x2 = -23.75

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = -23.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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