16x^2-10000x+90000=0

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Solution for 16x^2-10000x+90000=0 equation: 


Simplifying
16x2 + -10000x + 90000 = 0

Reorder the terms:
90000 + -10000x + 16x2 = 0

Solving
90000 + -10000x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '16'.
16(5625 + -625x + x2) = 0

Ignore the factor 16.

Subproblem 1
Set the factor '(5625 + -625x + x2)' equal to zero and attempt to solve:

Simplifying
5625 + -625x + x2 = 0

Solving
5625 + -625x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5625' to each side of the equation.
5625 + -625x + -5625 + x2 = 0 + -5625

Reorder the terms:
5625 + -5625 + -625x + x2 = 0 + -5625

Combine like terms: 5625 + -5625 = 0
0 + -625x + x2 = 0 + -5625
-625x + x2 = 0 + -5625

Combine like terms: 0 + -5625 = -5625
-625x + x2 = -5625

The x term is -625x.  Take half its coefficient (-312.5).
Square it (97656.25) and add it to both sides.

Add '97656.25' to each side of the equation.
-625x + 97656.25 + x2 = -5625 + 97656.25

Reorder the terms:
97656.25 + -625x + x2 = -5625 + 97656.25

Combine like terms: -5625 + 97656.25 = 92031.25
97656.25 + -625x + x2 = 92031.25

Factor a perfect square on the left side:
(x + -312.5)(x + -312.5) = 92031.25

Calculate the square root of the right side: 303.366527488

Break this problem into two subproblems by setting 
(x + -312.5) equal to 303.366527488 and -303.366527488.


Subproblem 1
x + -312.5 = 303.366527488

Simplifying
x + -312.5 = 303.366527488

Reorder the terms:
-312.5 + x = 303.366527488

Solving
-312.5 + x = 303.366527488

Solving for variable 'x'.

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

Add '312.5' to each side of the equation.
-312.5 + 312.5 + x = 303.366527488 + 312.5

Combine like terms: -312.5 + 312.5 = 0.0
0.0 + x = 303.366527488 + 312.5
x = 303.366527488 + 312.5

Combine like terms: 303.366527488 + 312.5 = 615.866527488
x = 615.866527488

Simplifying
x = 615.866527488


Subproblem 2
x + -312.5 = -303.366527488

Simplifying
x + -312.5 = -303.366527488

Reorder the terms:
-312.5 + x = -303.366527488

Solving
-312.5 + x = -303.366527488

Solving for variable 'x'.

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

Add '312.5' to each side of the equation.
-312.5 + 312.5 + x = -303.366527488 + 312.5

Combine like terms: -312.5 + 312.5 = 0.0
0.0 + x = -303.366527488 + 312.5
x = -303.366527488 + 312.5

Combine like terms: -303.366527488 + 312.5 = 9.133472512
x = 9.133472512

Simplifying
x = 9.133472512


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {615.866527488, 9.133472512}
Solution
x = {615.866527488, 9.133472512}

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