4x(4x)+14x=158

Solution for 4x(4x)+14x=158 equation:

Simplifying
4x(4x) + 14x = 158

Remove parenthesis around (4x)
4x * 4x + 14x = 158

Reorder the terms for easier multiplication:
4 * 4x * x + 14x = 158

Multiply 4 * 4
16x * x + 14x = 158

Multiply x * x
16x2 + 14x = 158

Reorder the terms:
14x + 16x2 = 158

Solving
14x + 16x2 = 158

Solving for variable 'x'.

Reorder the terms:
-158 + 14x + 16x2 = 158 + -158

Combine like terms: 158 + -158 = 0
-158 + 14x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-79 + 7x + 8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-79 + 7x + 8x2)' equal to zero and attempt to solve:

Simplifying
-79 + 7x + 8x2 = 0

Solving
-79 + 7x + 8x2 = 0

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

Divide each side by '8'.
-9.875 + 0.875x + x2 = 0

Move the constant term to the right:

Add '9.875' to each side of the equation.
-9.875 + 0.875x + 9.875 + x2 = 0 + 9.875

Reorder the terms:
-9.875 + 9.875 + 0.875x + x2 = 0 + 9.875

Combine like terms: -9.875 + 9.875 = 0.000
0.000 + 0.875x + x2 = 0 + 9.875
0.875x + x2 = 0 + 9.875

Combine like terms: 0 + 9.875 = 9.875
0.875x + x2 = 9.875

The x term is 0.875x.  Take half its coefficient (0.4375).
Square it (0.19140625) and add it to both sides.

Add '0.19140625' to each side of the equation.
0.875x + 0.19140625 + x2 = 9.875 + 0.19140625

Reorder the terms:
0.19140625 + 0.875x + x2 = 9.875 + 0.19140625

Combine like terms: 9.875 + 0.19140625 = 10.06640625
0.19140625 + 0.875x + x2 = 10.06640625

Factor a perfect square on the left side:
(x + 0.4375)(x + 0.4375) = 10.06640625

Calculate the square root of the right side: 3.172760037

Break this problem into two subproblems by setting 
(x + 0.4375) equal to 3.172760037 and -3.172760037.

Subproblem 1
x + 0.4375 = 3.172760037

Simplifying
x + 0.4375 = 3.172760037

Reorder the terms:
0.4375 + x = 3.172760037

Solving
0.4375 + x = 3.172760037

Solving for variable 'x'.

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

Add '-0.4375' to each side of the equation.
0.4375 + -0.4375 + x = 3.172760037 + -0.4375

Combine like terms: 0.4375 + -0.4375 = 0.0000
0.0000 + x = 3.172760037 + -0.4375
x = 3.172760037 + -0.4375

Combine like terms: 3.172760037 + -0.4375 = 2.735260037
x = 2.735260037

Simplifying
x = 2.735260037

Subproblem 2
x + 0.4375 = -3.172760037

Simplifying
x + 0.4375 = -3.172760037

Reorder the terms:
0.4375 + x = -3.172760037

Solving
0.4375 + x = -3.172760037

Solving for variable 'x'.

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

Add '-0.4375' to each side of the equation.
0.4375 + -0.4375 + x = -3.172760037 + -0.4375

Combine like terms: 0.4375 + -0.4375 = 0.0000
0.0000 + x = -3.172760037 + -0.4375
x = -3.172760037 + -0.4375

Combine like terms: -3.172760037 + -0.4375 = -3.610260037
x = -3.610260037

Simplifying
x = -3.610260037

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.735260037, -3.610260037}
Solution
x = {2.735260037, -3.610260037}