2x^2-2+14x=90

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Solution for 2x^2-2+14x=90 equation: 


Simplifying
2x2 + -2 + 14x = 90

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

Solving
-2 + 14x + 2x2 = 90

Solving for variable 'x'.

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

Combine like terms: -2 + -90 = -92
-92 + 14x + 2x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-92 + 14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-46 + 7x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-46 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
-46 + 7x + x2 = 0

Solving
-46 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '46' to each side of the equation.
-46 + 7x + 46 + x2 = 0 + 46

Reorder the terms:
-46 + 46 + 7x + x2 = 0 + 46

Combine like terms: -46 + 46 = 0
0 + 7x + x2 = 0 + 46
7x + x2 = 0 + 46

Combine like terms: 0 + 46 = 46
7x + x2 = 46

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 46 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 46 + 12.25

Combine like terms: 46 + 12.25 = 58.25
12.25 + 7x + x2 = 58.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 58.25

Calculate the square root of the right side: 7.632168761

Break this problem into two subproblems by setting 
(x + 3.5) equal to 7.632168761 and -7.632168761.


Subproblem 1
x + 3.5 = 7.632168761

Simplifying
x + 3.5 = 7.632168761

Reorder the terms:
3.5 + x = 7.632168761

Solving
3.5 + x = 7.632168761

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 7.632168761 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 7.632168761 + -3.5
x = 7.632168761 + -3.5

Combine like terms: 7.632168761 + -3.5 = 4.132168761
x = 4.132168761

Simplifying
x = 4.132168761


Subproblem 2
x + 3.5 = -7.632168761

Simplifying
x + 3.5 = -7.632168761

Reorder the terms:
3.5 + x = -7.632168761

Solving
3.5 + x = -7.632168761

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -7.632168761 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -7.632168761 + -3.5
x = -7.632168761 + -3.5

Combine like terms: -7.632168761 + -3.5 = -11.132168761
x = -11.132168761

Simplifying
x = -11.132168761


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.132168761, -11.132168761}
Solution
x = {4.132168761, -11.132168761}

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