2x^2+4x+2=90

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Solution for 2x^2+4x+2=90 equation: 


Simplifying
2x2 + 4x + 2 = 90

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

Solving
2 + 4x + 2x2 = 90

Solving for variable 'x'.

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

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

Combine like terms: 90 + -90 = 0
-88 + 4x + 2x2 = 0

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

Ignore the factor 2.

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

Simplifying
-44 + 2x + x2 = 0

Solving
-44 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + 2x + 44 + x2 = 0 + 44

Reorder the terms:
-44 + 44 + 2x + x2 = 0 + 44

Combine like terms: -44 + 44 = 0
0 + 2x + x2 = 0 + 44
2x + x2 = 0 + 44

Combine like terms: 0 + 44 = 44
2x + x2 = 44

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 44 + 1

Reorder the terms:
1 + 2x + x2 = 44 + 1

Combine like terms: 44 + 1 = 45
1 + 2x + x2 = 45

Factor a perfect square on the left side:
(x + 1)(x + 1) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(x + 1) equal to 6.708203933 and -6.708203933.


Subproblem 1
x + 1 = 6.708203933

Simplifying
x + 1 = 6.708203933

Reorder the terms:
1 + x = 6.708203933

Solving
1 + x = 6.708203933

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 6.708203933 + -1

Combine like terms: 1 + -1 = 0
0 + x = 6.708203933 + -1
x = 6.708203933 + -1

Combine like terms: 6.708203933 + -1 = 5.708203933
x = 5.708203933

Simplifying
x = 5.708203933


Subproblem 2
x + 1 = -6.708203933

Simplifying
x + 1 = -6.708203933

Reorder the terms:
1 + x = -6.708203933

Solving
1 + x = -6.708203933

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -6.708203933 + -1

Combine like terms: 1 + -1 = 0
0 + x = -6.708203933 + -1
x = -6.708203933 + -1

Combine like terms: -6.708203933 + -1 = -7.708203933
x = -7.708203933

Simplifying
x = -7.708203933


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.708203933, -7.708203933}
Solution
x = {5.708203933, -7.708203933}

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