4x^2-100x+176=0

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Solution for 4x^2-100x+176=0 equation: 


Simplifying
4x2 + -100x + 176 = 0

Reorder the terms:
176 + -100x + 4x2 = 0

Solving
176 + -100x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(44 + -25x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(44 + -25x + x2)' equal to zero and attempt to solve:

Simplifying
44 + -25x + x2 = 0

Solving
44 + -25x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-44' to each side of the equation.
44 + -25x + -44 + x2 = 0 + -44

Reorder the terms:
44 + -44 + -25x + x2 = 0 + -44

Combine like terms: 44 + -44 = 0
0 + -25x + x2 = 0 + -44
-25x + x2 = 0 + -44

Combine like terms: 0 + -44 = -44
-25x + x2 = -44

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 = -44 + 156.25

Reorder the terms:
156.25 + -25x + x2 = -44 + 156.25

Combine like terms: -44 + 156.25 = 112.25
156.25 + -25x + x2 = 112.25

Factor a perfect square on the left side:
(x + -12.5)(x + -12.5) = 112.25

Calculate the square root of the right side: 10.59481005

Break this problem into two subproblems by setting 
(x + -12.5) equal to 10.59481005 and -10.59481005.


Subproblem 1
x + -12.5 = 10.59481005

Simplifying
x + -12.5 = 10.59481005

Reorder the terms:
-12.5 + x = 10.59481005

Solving
-12.5 + x = 10.59481005

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 = 10.59481005 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = 10.59481005 + 12.5
x = 10.59481005 + 12.5

Combine like terms: 10.59481005 + 12.5 = 23.09481005
x = 23.09481005

Simplifying
x = 23.09481005


Subproblem 2
x + -12.5 = -10.59481005

Simplifying
x + -12.5 = -10.59481005

Reorder the terms:
-12.5 + x = -10.59481005

Solving
-12.5 + x = -10.59481005

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 = -10.59481005 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = -10.59481005 + 12.5
x = -10.59481005 + 12.5

Combine like terms: -10.59481005 + 12.5 = 1.90518995
x = 1.90518995

Simplifying
x = 1.90518995


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.09481005, 1.90518995}
Solution
x = {23.09481005, 1.90518995}

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