2x^2+42x-100=0

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Solution for 2x^2+42x-100=0 equation: 


Simplifying
2x2 + 42x + -100 = 0

Reorder the terms:
-100 + 42x + 2x2 = 0

Solving
-100 + 42x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + 21x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-50 + 21x + x2)' equal to zero and attempt to solve:

Simplifying
-50 + 21x + x2 = 0

Solving
-50 + 21x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + 21x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + 21x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + 21x + x2 = 0 + 50
21x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
21x + x2 = 50

The x term is 21x.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x + 110.25 + x2 = 50 + 110.25

Reorder the terms:
110.25 + 21x + x2 = 50 + 110.25

Combine like terms: 50 + 110.25 = 160.25
110.25 + 21x + x2 = 160.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 160.25

Calculate the square root of the right side: 12.658988901

Break this problem into two subproblems by setting 
(x + 10.5) equal to 12.658988901 and -12.658988901.


Subproblem 1
x + 10.5 = 12.658988901

Simplifying
x + 10.5 = 12.658988901

Reorder the terms:
10.5 + x = 12.658988901

Solving
10.5 + x = 12.658988901

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = 12.658988901 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 12.658988901 + -10.5
x = 12.658988901 + -10.5

Combine like terms: 12.658988901 + -10.5 = 2.158988901
x = 2.158988901

Simplifying
x = 2.158988901


Subproblem 2
x + 10.5 = -12.658988901

Simplifying
x + 10.5 = -12.658988901

Reorder the terms:
10.5 + x = -12.658988901

Solving
10.5 + x = -12.658988901

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = -12.658988901 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -12.658988901 + -10.5
x = -12.658988901 + -10.5

Combine like terms: -12.658988901 + -10.5 = -23.158988901
x = -23.158988901

Simplifying
x = -23.158988901


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.158988901, -23.158988901}
Solution
x = {2.158988901, -23.158988901}

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