2x^2-98x-1176=0

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Solution for 2x^2-98x-1176=0 equation: 


Simplifying
2x2 + -98x + -1176 = 0

Reorder the terms:
-1176 + -98x + 2x2 = 0

Solving
-1176 + -98x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-588 + -49x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-588 + -49x + x2)' equal to zero and attempt to solve:

Simplifying
-588 + -49x + x2 = 0

Solving
-588 + -49x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '588' to each side of the equation.
-588 + -49x + 588 + x2 = 0 + 588

Reorder the terms:
-588 + 588 + -49x + x2 = 0 + 588

Combine like terms: -588 + 588 = 0
0 + -49x + x2 = 0 + 588
-49x + x2 = 0 + 588

Combine like terms: 0 + 588 = 588
-49x + x2 = 588

The x term is -49x.  Take half its coefficient (-24.5).
Square it (600.25) and add it to both sides.

Add '600.25' to each side of the equation.
-49x + 600.25 + x2 = 588 + 600.25

Reorder the terms:
600.25 + -49x + x2 = 588 + 600.25

Combine like terms: 588 + 600.25 = 1188.25
600.25 + -49x + x2 = 1188.25

Factor a perfect square on the left side:
(x + -24.5)(x + -24.5) = 1188.25

Calculate the square root of the right side: 34.471002306

Break this problem into two subproblems by setting 
(x + -24.5) equal to 34.471002306 and -34.471002306.


Subproblem 1
x + -24.5 = 34.471002306

Simplifying
x + -24.5 = 34.471002306

Reorder the terms:
-24.5 + x = 34.471002306

Solving
-24.5 + x = 34.471002306

Solving for variable 'x'.

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

Add '24.5' to each side of the equation.
-24.5 + 24.5 + x = 34.471002306 + 24.5

Combine like terms: -24.5 + 24.5 = 0.0
0.0 + x = 34.471002306 + 24.5
x = 34.471002306 + 24.5

Combine like terms: 34.471002306 + 24.5 = 58.971002306
x = 58.971002306

Simplifying
x = 58.971002306


Subproblem 2
x + -24.5 = -34.471002306

Simplifying
x + -24.5 = -34.471002306

Reorder the terms:
-24.5 + x = -34.471002306

Solving
-24.5 + x = -34.471002306

Solving for variable 'x'.

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

Add '24.5' to each side of the equation.
-24.5 + 24.5 + x = -34.471002306 + 24.5

Combine like terms: -24.5 + 24.5 = 0.0
0.0 + x = -34.471002306 + 24.5
x = -34.471002306 + 24.5

Combine like terms: -34.471002306 + 24.5 = -9.971002306
x = -9.971002306

Simplifying
x = -9.971002306


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {58.971002306, -9.971002306}
Solution
x = {58.971002306, -9.971002306}

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