2x^2+28x-100=0

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Solution for 2x^2+28x-100=0 equation: 


Simplifying
2x2 + 28x + -100 = 0

Reorder the terms:
-100 + 28x + 2x2 = 0

Solving
-100 + 28x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + 14x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-50 + 14x + x2)' equal to zero and attempt to solve:

Simplifying
-50 + 14x + x2 = 0

Solving
-50 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + 14x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + 14x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + 14x + x2 = 0 + 50
14x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
14x + x2 = 50

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 = 50 + 49

Reorder the terms:
49 + 14x + x2 = 50 + 49

Combine like terms: 50 + 49 = 99
49 + 14x + x2 = 99

Factor a perfect square on the left side:
(x + 7)(x + 7) = 99

Calculate the square root of the right side: 9.949874371

Break this problem into two subproblems by setting 
(x + 7) equal to 9.949874371 and -9.949874371.


Subproblem 1
x + 7 = 9.949874371

Simplifying
x + 7 = 9.949874371

Reorder the terms:
7 + x = 9.949874371

Solving
7 + x = 9.949874371

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 = 9.949874371 + -7

Combine like terms: 7 + -7 = 0
0 + x = 9.949874371 + -7
x = 9.949874371 + -7

Combine like terms: 9.949874371 + -7 = 2.949874371
x = 2.949874371

Simplifying
x = 2.949874371


Subproblem 2
x + 7 = -9.949874371

Simplifying
x + 7 = -9.949874371

Reorder the terms:
7 + x = -9.949874371

Solving
7 + x = -9.949874371

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 = -9.949874371 + -7

Combine like terms: 7 + -7 = 0
0 + x = -9.949874371 + -7
x = -9.949874371 + -7

Combine like terms: -9.949874371 + -7 = -16.949874371
x = -16.949874371

Simplifying
x = -16.949874371


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.949874371, -16.949874371}
Solution
x = {2.949874371, -16.949874371}

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