2x*x+(-8x)=4

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Solution for 2x*x+(-8x)=4 equation: 


Simplifying
2x * x + (-8x) = 4

Multiply x * x
2x2 + (-8x) = 4

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

Solving
(-8x) + 2x2 = 4

Solving for variable 'x'.

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

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

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + (-4x) + x2)' equal to zero and attempt to solve:

Simplifying
-2 + (-4x) + x2 = 0

Solving
-2 + (-4x) + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + (-4x) + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + (-4x) + x2 = 0 + 2

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

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

The x term is (-4x).  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
(-4x) + 4 + x2 = 2 + 4

Reorder the terms:
4 + (-4x) + x2 = 2 + 4

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

Factor a perfect square on the left side:
(x + -2)(x + -2) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + -2) equal to 2.449489743 and -2.449489743.


Subproblem 1
x + -2 = 2.449489743

Simplifying
x + -2 = 2.449489743

Reorder the terms:
-2 + x = 2.449489743

Solving
-2 + x = 2.449489743

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 2.449489743 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.449489743 + 2
x = 2.449489743 + 2

Combine like terms: 2.449489743 + 2 = 4.449489743
x = 4.449489743

Simplifying
x = 4.449489743


Subproblem 2
x + -2 = -2.449489743

Simplifying
x + -2 = -2.449489743

Reorder the terms:
-2 + x = -2.449489743

Solving
-2 + x = -2.449489743

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -2.449489743 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.449489743 + 2
x = -2.449489743 + 2

Combine like terms: -2.449489743 + 2 = -0.449489743
x = -0.449489743

Simplifying
x = -0.449489743


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.449489743, -0.449489743}
Solution
x = {4.449489743, -0.449489743}

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