0=-180+100(x)-4x^2

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Solution for 0=-180+100(x)-4x^2 equation: 


Simplifying
0 = -180 + 100(x) + -4x2

Solving
0 = -180 + 100x + -4x2

Solving for variable 'x'.

Combine like terms: 0 + 180 = 180
180 + -100x + 4x2 = -180 + 100x + -4x2 + 180 + -100x + 4x2

Reorder the terms:
180 + -100x + 4x2 = -180 + 180 + 100x + -100x + -4x2 + 4x2

Combine like terms: -180 + 180 = 0
180 + -100x + 4x2 = 0 + 100x + -100x + -4x2 + 4x2
180 + -100x + 4x2 = 100x + -100x + -4x2 + 4x2

Combine like terms: 100x + -100x = 0
180 + -100x + 4x2 = 0 + -4x2 + 4x2
180 + -100x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
180 + -100x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(45 + -25x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(45 + -25x + x2)' equal to zero and attempt to solve:

Simplifying
45 + -25x + x2 = 0

Solving
45 + -25x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-45' to each side of the equation.
45 + -25x + -45 + x2 = 0 + -45

Reorder the terms:
45 + -45 + -25x + x2 = 0 + -45

Combine like terms: 45 + -45 = 0
0 + -25x + x2 = 0 + -45
-25x + x2 = 0 + -45

Combine like terms: 0 + -45 = -45
-25x + x2 = -45

The x term is -25x.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25x + 156.25 + x2 = -45 + 156.25

Reorder the terms:
156.25 + -25x + x2 = -45 + 156.25

Combine like terms: -45 + 156.25 = 111.25
156.25 + -25x + x2 = 111.25

Factor a perfect square on the left side:
(x + -12.5)(x + -12.5) = 111.25

Calculate the square root of the right side: 10.547511555

Break this problem into two subproblems by setting 
(x + -12.5) equal to 10.547511555 and -10.547511555.


Subproblem 1
x + -12.5 = 10.547511555

Simplifying
x + -12.5 = 10.547511555

Reorder the terms:
-12.5 + x = 10.547511555

Solving
-12.5 + x = 10.547511555

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x = 10.547511555 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = 10.547511555 + 12.5
x = 10.547511555 + 12.5

Combine like terms: 10.547511555 + 12.5 = 23.047511555
x = 23.047511555

Simplifying
x = 23.047511555


Subproblem 2
x + -12.5 = -10.547511555

Simplifying
x + -12.5 = -10.547511555

Reorder the terms:
-12.5 + x = -10.547511555

Solving
-12.5 + x = -10.547511555

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x = -10.547511555 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = -10.547511555 + 12.5
x = -10.547511555 + 12.5

Combine like terms: -10.547511555 + 12.5 = 1.952488445
x = 1.952488445

Simplifying
x = 1.952488445


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.047511555, 1.952488445}
Solution
x = {23.047511555, 1.952488445}

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