2x^2+42x+68=0

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Solution for 2x^2+42x+68=0 equation: 


Simplifying
2x2 + 42x + 68 = 0

Reorder the terms:
68 + 42x + 2x2 = 0

Solving
68 + 42x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(34 + 21x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(34 + 21x + x2)' equal to zero and attempt to solve:

Simplifying
34 + 21x + x2 = 0

Solving
34 + 21x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-34' to each side of the equation.
34 + 21x + -34 + x2 = 0 + -34

Reorder the terms:
34 + -34 + 21x + x2 = 0 + -34

Combine like terms: 34 + -34 = 0
0 + 21x + x2 = 0 + -34
21x + x2 = 0 + -34

Combine like terms: 0 + -34 = -34
21x + x2 = -34

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 = -34 + 110.25

Reorder the terms:
110.25 + 21x + x2 = -34 + 110.25

Combine like terms: -34 + 110.25 = 76.25
110.25 + 21x + x2 = 76.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 76.25

Calculate the square root of the right side: 8.732124598

Break this problem into two subproblems by setting 
(x + 10.5) equal to 8.732124598 and -8.732124598.


Subproblem 1
x + 10.5 = 8.732124598

Simplifying
x + 10.5 = 8.732124598

Reorder the terms:
10.5 + x = 8.732124598

Solving
10.5 + x = 8.732124598

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 = 8.732124598 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 8.732124598 + -10.5
x = 8.732124598 + -10.5

Combine like terms: 8.732124598 + -10.5 = -1.767875402
x = -1.767875402

Simplifying
x = -1.767875402


Subproblem 2
x + 10.5 = -8.732124598

Simplifying
x + 10.5 = -8.732124598

Reorder the terms:
10.5 + x = -8.732124598

Solving
10.5 + x = -8.732124598

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 = -8.732124598 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -8.732124598 + -10.5
x = -8.732124598 + -10.5

Combine like terms: -8.732124598 + -10.5 = -19.232124598
x = -19.232124598

Simplifying
x = -19.232124598


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.767875402, -19.232124598}
Solution
x = {-1.767875402, -19.232124598}

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