4x^2-41x+98=0

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Solution for 4x^2-41x+98=0 equation: 


Simplifying
4x2 + -41x + 98 = 0

Reorder the terms:
98 + -41x + 4x2 = 0

Solving
98 + -41x + 4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
24.5 + -10.25x + x2 = 0

Move the constant term to the right:

Add '-24.5' to each side of the equation.
24.5 + -10.25x + -24.5 + x2 = 0 + -24.5

Reorder the terms:
24.5 + -24.5 + -10.25x + x2 = 0 + -24.5

Combine like terms: 24.5 + -24.5 = 0.0
0.0 + -10.25x + x2 = 0 + -24.5
-10.25x + x2 = 0 + -24.5

Combine like terms: 0 + -24.5 = -24.5
-10.25x + x2 = -24.5

The x term is -10.25x.  Take half its coefficient (-5.125).
Square it (26.265625) and add it to both sides.

Add '26.265625' to each side of the equation.
-10.25x + 26.265625 + x2 = -24.5 + 26.265625

Reorder the terms:
26.265625 + -10.25x + x2 = -24.5 + 26.265625

Combine like terms: -24.5 + 26.265625 = 1.765625
26.265625 + -10.25x + x2 = 1.765625

Factor a perfect square on the left side:
(x + -5.125)(x + -5.125) = 1.765625

Calculate the square root of the right side: 1.328768227

Break this problem into two subproblems by setting 
(x + -5.125) equal to 1.328768227 and -1.328768227.


Subproblem 1
x + -5.125 = 1.328768227

Simplifying
x + -5.125 = 1.328768227

Reorder the terms:
-5.125 + x = 1.328768227

Solving
-5.125 + x = 1.328768227

Solving for variable 'x'.

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

Add '5.125' to each side of the equation.
-5.125 + 5.125 + x = 1.328768227 + 5.125

Combine like terms: -5.125 + 5.125 = 0.000
0.000 + x = 1.328768227 + 5.125
x = 1.328768227 + 5.125

Combine like terms: 1.328768227 + 5.125 = 6.453768227
x = 6.453768227

Simplifying
x = 6.453768227


Subproblem 2
x + -5.125 = -1.328768227

Simplifying
x + -5.125 = -1.328768227

Reorder the terms:
-5.125 + x = -1.328768227

Solving
-5.125 + x = -1.328768227

Solving for variable 'x'.

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

Add '5.125' to each side of the equation.
-5.125 + 5.125 + x = -1.328768227 + 5.125

Combine like terms: -5.125 + 5.125 = 0.000
0.000 + x = -1.328768227 + 5.125
x = -1.328768227 + 5.125

Combine like terms: -1.328768227 + 5.125 = 3.796231773
x = 3.796231773

Simplifying
x = 3.796231773


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.453768227, 3.796231773}

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