4x^2-180x+1000=0

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Solution for 4x^2-180x+1000=0 equation: 


Simplifying
4x2 + -180x + 1000 = 0

Reorder the terms:
1000 + -180x + 4x2 = 0

Solving
1000 + -180x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(250 + -45x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(250 + -45x + x2)' equal to zero and attempt to solve:

Simplifying
250 + -45x + x2 = 0

Solving
250 + -45x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-250' to each side of the equation.
250 + -45x + -250 + x2 = 0 + -250

Reorder the terms:
250 + -250 + -45x + x2 = 0 + -250

Combine like terms: 250 + -250 = 0
0 + -45x + x2 = 0 + -250
-45x + x2 = 0 + -250

Combine like terms: 0 + -250 = -250
-45x + x2 = -250

The x term is -45x.  Take half its coefficient (-22.5).
Square it (506.25) and add it to both sides.

Add '506.25' to each side of the equation.
-45x + 506.25 + x2 = -250 + 506.25

Reorder the terms:
506.25 + -45x + x2 = -250 + 506.25

Combine like terms: -250 + 506.25 = 256.25
506.25 + -45x + x2 = 256.25

Factor a perfect square on the left side:
(x + -22.5)(x + -22.5) = 256.25

Calculate the square root of the right side: 16.007810594

Break this problem into two subproblems by setting 
(x + -22.5) equal to 16.007810594 and -16.007810594.


Subproblem 1
x + -22.5 = 16.007810594

Simplifying
x + -22.5 = 16.007810594

Reorder the terms:
-22.5 + x = 16.007810594

Solving
-22.5 + x = 16.007810594

Solving for variable 'x'.

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

Add '22.5' to each side of the equation.
-22.5 + 22.5 + x = 16.007810594 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + x = 16.007810594 + 22.5
x = 16.007810594 + 22.5

Combine like terms: 16.007810594 + 22.5 = 38.507810594
x = 38.507810594

Simplifying
x = 38.507810594


Subproblem 2
x + -22.5 = -16.007810594

Simplifying
x + -22.5 = -16.007810594

Reorder the terms:
-22.5 + x = -16.007810594

Solving
-22.5 + x = -16.007810594

Solving for variable 'x'.

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

Add '22.5' to each side of the equation.
-22.5 + 22.5 + x = -16.007810594 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + x = -16.007810594 + 22.5
x = -16.007810594 + 22.5

Combine like terms: -16.007810594 + 22.5 = 6.492189406
x = 6.492189406

Simplifying
x = 6.492189406


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {38.507810594, 6.492189406}
Solution
x = {38.507810594, 6.492189406}

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