4x^2-98x+150=0

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Solution for 4x^2-98x+150=0 equation: 


Simplifying
4x2 + -98x + 150 = 0

Reorder the terms:
150 + -98x + 4x2 = 0

Solving
150 + -98x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(75 + -49x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(75 + -49x + 2x2)' equal to zero and attempt to solve:

Simplifying
75 + -49x + 2x2 = 0

Solving
75 + -49x + 2x2 = 0

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

Divide each side by '2'.
37.5 + -24.5x + x2 = 0

Move the constant term to the right:

Add '-37.5' to each side of the equation.
37.5 + -24.5x + -37.5 + x2 = 0 + -37.5

Reorder the terms:
37.5 + -37.5 + -24.5x + x2 = 0 + -37.5

Combine like terms: 37.5 + -37.5 = 0.0
0.0 + -24.5x + x2 = 0 + -37.5
-24.5x + x2 = 0 + -37.5

Combine like terms: 0 + -37.5 = -37.5
-24.5x + x2 = -37.5

The x term is -24.5x.  Take half its coefficient (-12.25).
Square it (150.0625) and add it to both sides.

Add '150.0625' to each side of the equation.
-24.5x + 150.0625 + x2 = -37.5 + 150.0625

Reorder the terms:
150.0625 + -24.5x + x2 = -37.5 + 150.0625

Combine like terms: -37.5 + 150.0625 = 112.5625
150.0625 + -24.5x + x2 = 112.5625

Factor a perfect square on the left side:
(x + -12.25)(x + -12.25) = 112.5625

Calculate the square root of the right side: 10.609547587

Break this problem into two subproblems by setting 
(x + -12.25) equal to 10.609547587 and -10.609547587.


Subproblem 1
x + -12.25 = 10.609547587

Simplifying
x + -12.25 = 10.609547587

Reorder the terms:
-12.25 + x = 10.609547587

Solving
-12.25 + x = 10.609547587

Solving for variable 'x'.

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

Add '12.25' to each side of the equation.
-12.25 + 12.25 + x = 10.609547587 + 12.25

Combine like terms: -12.25 + 12.25 = 0.00
0.00 + x = 10.609547587 + 12.25
x = 10.609547587 + 12.25

Combine like terms: 10.609547587 + 12.25 = 22.859547587
x = 22.859547587

Simplifying
x = 22.859547587


Subproblem 2
x + -12.25 = -10.609547587

Simplifying
x + -12.25 = -10.609547587

Reorder the terms:
-12.25 + x = -10.609547587

Solving
-12.25 + x = -10.609547587

Solving for variable 'x'.

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

Add '12.25' to each side of the equation.
-12.25 + 12.25 + x = -10.609547587 + 12.25

Combine like terms: -12.25 + 12.25 = 0.00
0.00 + x = -10.609547587 + 12.25
x = -10.609547587 + 12.25

Combine like terms: -10.609547587 + 12.25 = 1.640452413
x = 1.640452413

Simplifying
x = 1.640452413


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.859547587, 1.640452413}
Solution
x = {22.859547587, 1.640452413}

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