2x^2-28x-140=0

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Solution for 2x^2-28x-140=0 equation: 


Simplifying
2x2 + -28x + -140 = 0

Reorder the terms:
-140 + -28x + 2x2 = 0

Solving
-140 + -28x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-70 + -14x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-70 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
-70 + -14x + x2 = 0

Solving
-70 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + -14x + 70 + x2 = 0 + 70

Reorder the terms:
-70 + 70 + -14x + x2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + -14x + x2 = 0 + 70
-14x + x2 = 0 + 70

Combine like terms: 0 + 70 = 70
-14x + x2 = 70

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = 70 + 49

Reorder the terms:
49 + -14x + x2 = 70 + 49

Combine like terms: 70 + 49 = 119
49 + -14x + x2 = 119

Factor a perfect square on the left side:
(x + -7)(x + -7) = 119

Calculate the square root of the right side: 10.908712115

Break this problem into two subproblems by setting 
(x + -7) equal to 10.908712115 and -10.908712115.


Subproblem 1
x + -7 = 10.908712115

Simplifying
x + -7 = 10.908712115

Reorder the terms:
-7 + x = 10.908712115

Solving
-7 + x = 10.908712115

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 10.908712115 + 7

Combine like terms: -7 + 7 = 0
0 + x = 10.908712115 + 7
x = 10.908712115 + 7

Combine like terms: 10.908712115 + 7 = 17.908712115
x = 17.908712115

Simplifying
x = 17.908712115


Subproblem 2
x + -7 = -10.908712115

Simplifying
x + -7 = -10.908712115

Reorder the terms:
-7 + x = -10.908712115

Solving
-7 + x = -10.908712115

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -10.908712115 + 7

Combine like terms: -7 + 7 = 0
0 + x = -10.908712115 + 7
x = -10.908712115 + 7

Combine like terms: -10.908712115 + 7 = -3.908712115
x = -3.908712115

Simplifying
x = -3.908712115


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.908712115, -3.908712115}
Solution
x = {17.908712115, -3.908712115}

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