2x(2x)+2+14x=90

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Solution for 2x(2x)+2+14x=90 equation: 


Simplifying
2x(2x) + 2 + 14x = 90

Remove parenthesis around (2x)
2x * 2x + 2 + 14x = 90

Reorder the terms for easier multiplication:
2 * 2x * x + 2 + 14x = 90

Multiply 2 * 2
4x * x + 2 + 14x = 90

Multiply x * x
4x2 + 2 + 14x = 90

Reorder the terms:
2 + 14x + 4x2 = 90

Solving
2 + 14x + 4x2 = 90

Solving for variable 'x'.

Reorder the terms:
2 + -90 + 14x + 4x2 = 90 + -90

Combine like terms: 2 + -90 = -88
-88 + 14x + 4x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-88 + 14x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-44 + 7x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-44 + 7x + 2x2)' equal to zero and attempt to solve:

Simplifying
-44 + 7x + 2x2 = 0

Solving
-44 + 7x + 2x2 = 0

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

Divide each side by '2'.
-22 + 3.5x + x2 = 0

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + 3.5x + 22 + x2 = 0 + 22

Reorder the terms:
-22 + 22 + 3.5x + x2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + 3.5x + x2 = 0 + 22
3.5x + x2 = 0 + 22

Combine like terms: 0 + 22 = 22
3.5x + x2 = 22

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 = 22 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 22 + 3.0625

Combine like terms: 22 + 3.0625 = 25.0625
3.0625 + 3.5x + x2 = 25.0625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 25.0625

Calculate the square root of the right side: 5.006246099

Break this problem into two subproblems by setting 
(x + 1.75) equal to 5.006246099 and -5.006246099.


Subproblem 1
x + 1.75 = 5.006246099

Simplifying
x + 1.75 = 5.006246099

Reorder the terms:
1.75 + x = 5.006246099

Solving
1.75 + x = 5.006246099

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 = 5.006246099 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 5.006246099 + -1.75
x = 5.006246099 + -1.75

Combine like terms: 5.006246099 + -1.75 = 3.256246099
x = 3.256246099

Simplifying
x = 3.256246099


Subproblem 2
x + 1.75 = -5.006246099

Simplifying
x + 1.75 = -5.006246099

Reorder the terms:
1.75 + x = -5.006246099

Solving
1.75 + x = -5.006246099

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 = -5.006246099 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -5.006246099 + -1.75
x = -5.006246099 + -1.75

Combine like terms: -5.006246099 + -1.75 = -6.756246099
x = -6.756246099

Simplifying
x = -6.756246099


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.256246099, -6.756246099}
Solution
x = {3.256246099, -6.756246099}

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