2x(2x)+14x=158

Solution for 2x(2x)+14x=158 equation:

Simplifying
2x(2x) + 14x = 158

Remove parenthesis around (2x)
2x * 2x + 14x = 158

Reorder the terms for easier multiplication:
2 * 2x * x + 14x = 158

Multiply 2 * 2
4x * x + 14x = 158

Multiply x * x
4x2 + 14x = 158

Reorder the terms:
14x + 4x2 = 158

Solving
14x + 4x2 = 158

Solving for variable 'x'.

Reorder the terms:
-158 + 14x + 4x2 = 158 + -158

Combine like terms: 158 + -158 = 0
-158 + 14x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-79 + 7x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-79 + 7x + 2x2)' equal to zero and attempt to solve:

Simplifying
-79 + 7x + 2x2 = 0

Solving
-79 + 7x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-39.5 + 3.5x + x2 = 0

Move the constant term to the right:

Add '39.5' to each side of the equation.
-39.5 + 3.5x + 39.5 + x2 = 0 + 39.5

Reorder the terms:
-39.5 + 39.5 + 3.5x + x2 = 0 + 39.5

Combine like terms: -39.5 + 39.5 = 0.0
0.0 + 3.5x + x2 = 0 + 39.5
3.5x + x2 = 0 + 39.5

Combine like terms: 0 + 39.5 = 39.5
3.5x + x2 = 39.5

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 39.5 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 39.5 + 3.0625

Combine like terms: 39.5 + 3.0625 = 42.5625
3.0625 + 3.5x + x2 = 42.5625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 42.5625

Calculate the square root of the right side: 6.523994175

Break this problem into two subproblems by setting 
(x + 1.75) equal to 6.523994175 and -6.523994175.

Subproblem 1
x + 1.75 = 6.523994175

Simplifying
x + 1.75 = 6.523994175

Reorder the terms:
1.75 + x = 6.523994175

Solving
1.75 + x = 6.523994175

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 6.523994175 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 6.523994175 + -1.75
x = 6.523994175 + -1.75

Combine like terms: 6.523994175 + -1.75 = 4.773994175
x = 4.773994175

Simplifying
x = 4.773994175

Subproblem 2
x + 1.75 = -6.523994175

Simplifying
x + 1.75 = -6.523994175

Reorder the terms:
1.75 + x = -6.523994175

Solving
1.75 + x = -6.523994175

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -6.523994175 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -6.523994175 + -1.75
x = -6.523994175 + -1.75

Combine like terms: -6.523994175 + -1.75 = -8.273994175
x = -8.273994175

Simplifying
x = -8.273994175

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.773994175, -8.273994175}
Solution
x = {4.773994175, -8.273994175}