2x^2+18x+20=0

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Solution for 2x^2+18x+20=0 equation: 


Simplifying
2x2 + 18x + 20 = 0

Reorder the terms:
20 + 18x + 2x2 = 0

Solving
20 + 18x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + 9x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(10 + 9x + x2)' equal to zero and attempt to solve:

Simplifying
10 + 9x + x2 = 0

Solving
10 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 9x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + 9x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 9x + x2 = 0 + -10
9x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
9x + x2 = -10

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = -10 + 20.25

Reorder the terms:
20.25 + 9x + x2 = -10 + 20.25

Combine like terms: -10 + 20.25 = 10.25
20.25 + 9x + x2 = 10.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + 4.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
x + 4.5 = 3.201562119

Simplifying
x + 4.5 = 3.201562119

Reorder the terms:
4.5 + x = 3.201562119

Solving
4.5 + x = 3.201562119

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 3.201562119 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 3.201562119 + -4.5
x = 3.201562119 + -4.5

Combine like terms: 3.201562119 + -4.5 = -1.298437881
x = -1.298437881

Simplifying
x = -1.298437881


Subproblem 2
x + 4.5 = -3.201562119

Simplifying
x + 4.5 = -3.201562119

Reorder the terms:
4.5 + x = -3.201562119

Solving
4.5 + x = -3.201562119

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -3.201562119 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -3.201562119 + -4.5
x = -3.201562119 + -4.5

Combine like terms: -3.201562119 + -4.5 = -7.701562119
x = -7.701562119

Simplifying
x = -7.701562119


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.298437881, -7.701562119}
Solution
x = {-1.298437881, -7.701562119}

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