2x^2-14x-298=0

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Solution for 2x^2-14x-298=0 equation: 


Simplifying
2x2 + -14x + -298 = 0

Reorder the terms:
-298 + -14x + 2x2 = 0

Solving
-298 + -14x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-149 + -7x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-149 + -7x + x2)' equal to zero and attempt to solve:

Simplifying
-149 + -7x + x2 = 0

Solving
-149 + -7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '149' to each side of the equation.
-149 + -7x + 149 + x2 = 0 + 149

Reorder the terms:
-149 + 149 + -7x + x2 = 0 + 149

Combine like terms: -149 + 149 = 0
0 + -7x + x2 = 0 + 149
-7x + x2 = 0 + 149

Combine like terms: 0 + 149 = 149
-7x + x2 = 149

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 149 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 149 + 12.25

Combine like terms: 149 + 12.25 = 161.25
12.25 + -7x + x2 = 161.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 161.25

Calculate the square root of the right side: 12.698425099

Break this problem into two subproblems by setting 
(x + -3.5) equal to 12.698425099 and -12.698425099.


Subproblem 1
x + -3.5 = 12.698425099

Simplifying
x + -3.5 = 12.698425099

Reorder the terms:
-3.5 + x = 12.698425099

Solving
-3.5 + x = 12.698425099

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 12.698425099 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 12.698425099 + 3.5
x = 12.698425099 + 3.5

Combine like terms: 12.698425099 + 3.5 = 16.198425099
x = 16.198425099

Simplifying
x = 16.198425099


Subproblem 2
x + -3.5 = -12.698425099

Simplifying
x + -3.5 = -12.698425099

Reorder the terms:
-3.5 + x = -12.698425099

Solving
-3.5 + x = -12.698425099

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -12.698425099 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -12.698425099 + 3.5
x = -12.698425099 + 3.5

Combine like terms: -12.698425099 + 3.5 = -9.198425099
x = -9.198425099

Simplifying
x = -9.198425099


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.198425099, -9.198425099}
Solution
x = {16.198425099, -9.198425099}

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