2x^2-4x+4=3+4

Solution for 2x^2-4x+4=3+4 equation:

Simplifying
2x2 + -4x + 4 = 3 + 4

Reorder the terms:
4 + -4x + 2x2 = 3 + 4

Combine like terms: 3 + 4 = 7
4 + -4x + 2x2 = 7

Solving
4 + -4x + 2x2 = 7

Solving for variable 'x'.

Reorder the terms:
4 + -7 + -4x + 2x2 = 7 + -7

Combine like terms: 4 + -7 = -3
-3 + -4x + 2x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-3 + -4x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-1.5 + -2x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -2x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -2x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -2x + x2 = 0 + 1.5
-2x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-2x + x2 = 1.5

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 = 1.5 + 1

Reorder the terms:
1 + -2x + x2 = 1.5 + 1

Combine like terms: 1.5 + 1 = 2.5
1 + -2x + x2 = 2.5

Factor a perfect square on the left side:
(x + -1)(x + -1) = 2.5

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(x + -1) equal to 1.58113883 and -1.58113883.

Subproblem 1
x + -1 = 1.58113883

Simplifying
x + -1 = 1.58113883

Reorder the terms:
-1 + x = 1.58113883

Solving
-1 + x = 1.58113883

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 = 1.58113883 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.58113883 + 1
x = 1.58113883 + 1

Combine like terms: 1.58113883 + 1 = 2.58113883
x = 2.58113883

Simplifying
x = 2.58113883

Subproblem 2
x + -1 = -1.58113883

Simplifying
x + -1 = -1.58113883

Reorder the terms:
-1 + x = -1.58113883

Solving
-1 + x = -1.58113883

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 = -1.58113883 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.58113883 + 1
x = -1.58113883 + 1

Combine like terms: -1.58113883 + 1 = -0.58113883
x = -0.58113883

Simplifying
x = -0.58113883

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.58113883, -0.58113883}