4x^2+6x=8-2x

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Solution for 4x^2+6x=8-2x equation: 


Simplifying
4x2 + 6x = 8 + -2x

Reorder the terms:
6x + 4x2 = 8 + -2x

Solving
6x + 4x2 = 8 + -2x

Solving for variable 'x'.

Reorder the terms:
-8 + 6x + 2x + 4x2 = 8 + -2x + -8 + 2x

Combine like terms: 6x + 2x = 8x
-8 + 8x + 4x2 = 8 + -2x + -8 + 2x

Reorder the terms:
-8 + 8x + 4x2 = 8 + -8 + -2x + 2x

Combine like terms: 8 + -8 = 0
-8 + 8x + 4x2 = 0 + -2x + 2x
-8 + 8x + 4x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-8 + 8x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + 2x + x2) = 0

Ignore the factor 4.

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

Simplifying
-2 + 2x + x2 = 0

Solving
-2 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 2 + 1

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

Combine like terms: 2 + 1 = 3
1 + 2x + x2 = 3

Factor a perfect square on the left side:
(x + 1)(x + 1) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + 1) equal to 1.732050808 and -1.732050808.


Subproblem 1
x + 1 = 1.732050808

Simplifying
x + 1 = 1.732050808

Reorder the terms:
1 + x = 1.732050808

Solving
1 + x = 1.732050808

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 = 1.732050808 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.732050808 + -1
x = 1.732050808 + -1

Combine like terms: 1.732050808 + -1 = 0.732050808
x = 0.732050808

Simplifying
x = 0.732050808


Subproblem 2
x + 1 = -1.732050808

Simplifying
x + 1 = -1.732050808

Reorder the terms:
1 + x = -1.732050808

Solving
1 + x = -1.732050808

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 = -1.732050808 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.732050808 + -1
x = -1.732050808 + -1

Combine like terms: -1.732050808 + -1 = -2.732050808
x = -2.732050808

Simplifying
x = -2.732050808


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.732050808, -2.732050808}
Solution
x = {0.732050808, -2.732050808}

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