2x^2+14x+20=90

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Solution for 2x^2+14x+20=90 equation: 


Simplifying
2x2 + 14x + 20 = 90

Reorder the terms:
20 + 14x + 2x2 = 90

Solving
20 + 14x + 2x2 = 90

Solving for variable 'x'.

Reorder the terms:
20 + -90 + 14x + 2x2 = 90 + -90

Combine like terms: 20 + -90 = -70
-70 + 14x + 2x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-70 + 14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-35 + 7x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-35 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
-35 + 7x + x2 = 0

Solving
-35 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + 7x + 35 + x2 = 0 + 35

Reorder the terms:
-35 + 35 + 7x + x2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + 7x + x2 = 0 + 35
7x + x2 = 0 + 35

Combine like terms: 0 + 35 = 35
7x + x2 = 35

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 = 35 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 35 + 12.25

Combine like terms: 35 + 12.25 = 47.25
12.25 + 7x + x2 = 47.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 47.25

Calculate the square root of the right side: 6.873863542

Break this problem into two subproblems by setting 
(x + 3.5) equal to 6.873863542 and -6.873863542.


Subproblem 1
x + 3.5 = 6.873863542

Simplifying
x + 3.5 = 6.873863542

Reorder the terms:
3.5 + x = 6.873863542

Solving
3.5 + x = 6.873863542

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 = 6.873863542 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 6.873863542 + -3.5
x = 6.873863542 + -3.5

Combine like terms: 6.873863542 + -3.5 = 3.373863542
x = 3.373863542

Simplifying
x = 3.373863542


Subproblem 2
x + 3.5 = -6.873863542

Simplifying
x + 3.5 = -6.873863542

Reorder the terms:
3.5 + x = -6.873863542

Solving
3.5 + x = -6.873863542

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 = -6.873863542 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -6.873863542 + -3.5
x = -6.873863542 + -3.5

Combine like terms: -6.873863542 + -3.5 = -10.373863542
x = -10.373863542

Simplifying
x = -10.373863542


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.373863542, -10.373863542}
Solution
x = {3.373863542, -10.373863542}

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