4x^2-100x+296=0

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Solution for 4x^2-100x+296=0 equation: 


Simplifying
4x2 + -100x + 296 = 0

Reorder the terms:
296 + -100x + 4x2 = 0

Solving
296 + -100x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(74 + -25x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(74 + -25x + x2)' equal to zero and attempt to solve:

Simplifying
74 + -25x + x2 = 0

Solving
74 + -25x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-74' to each side of the equation.
74 + -25x + -74 + x2 = 0 + -74

Reorder the terms:
74 + -74 + -25x + x2 = 0 + -74

Combine like terms: 74 + -74 = 0
0 + -25x + x2 = 0 + -74
-25x + x2 = 0 + -74

Combine like terms: 0 + -74 = -74
-25x + x2 = -74

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 = -74 + 156.25

Reorder the terms:
156.25 + -25x + x2 = -74 + 156.25

Combine like terms: -74 + 156.25 = 82.25
156.25 + -25x + x2 = 82.25

Factor a perfect square on the left side:
(x + -12.5)(x + -12.5) = 82.25

Calculate the square root of the right side: 9.069178574

Break this problem into two subproblems by setting 
(x + -12.5) equal to 9.069178574 and -9.069178574.


Subproblem 1
x + -12.5 = 9.069178574

Simplifying
x + -12.5 = 9.069178574

Reorder the terms:
-12.5 + x = 9.069178574

Solving
-12.5 + x = 9.069178574

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 = 9.069178574 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = 9.069178574 + 12.5
x = 9.069178574 + 12.5

Combine like terms: 9.069178574 + 12.5 = 21.569178574
x = 21.569178574

Simplifying
x = 21.569178574


Subproblem 2
x + -12.5 = -9.069178574

Simplifying
x + -12.5 = -9.069178574

Reorder the terms:
-12.5 + x = -9.069178574

Solving
-12.5 + x = -9.069178574

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 = -9.069178574 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = -9.069178574 + 12.5
x = -9.069178574 + 12.5

Combine like terms: -9.069178574 + 12.5 = 3.430821426
x = 3.430821426

Simplifying
x = 3.430821426


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.569178574, 3.430821426}
Solution
x = {21.569178574, 3.430821426}

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