3x^2+(x+1)(x+1)=(x+2)(x+2)

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Solution for 3x^2+(x+1)(x+1)=(x+2)(x+2) equation:


Simplifying
3x2 + (x + 1)(x + 1) = (x + 2)(x + 2)

Reorder the terms:
3x2 + (1 + x)(x + 1) = (x + 2)(x + 2)

Reorder the terms:
3x2 + (1 + x)(1 + x) = (x + 2)(x + 2)

Multiply (1 + x) * (1 + x)
3x2 + (1(1 + x) + x(1 + x)) = (x + 2)(x + 2)
3x2 + ((1 * 1 + x * 1) + x(1 + x)) = (x + 2)(x + 2)
3x2 + ((1 + 1x) + x(1 + x)) = (x + 2)(x + 2)
3x2 + (1 + 1x + (1 * x + x * x)) = (x + 2)(x + 2)
3x2 + (1 + 1x + (1x + x2)) = (x + 2)(x + 2)

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

Reorder the terms:
1 + 2x + 3x2 + x2 = (x + 2)(x + 2)

Combine like terms: 3x2 + x2 = 4x2
1 + 2x + 4x2 = (x + 2)(x + 2)

Reorder the terms:
1 + 2x + 4x2 = (2 + x)(x + 2)

Reorder the terms:
1 + 2x + 4x2 = (2 + x)(2 + x)

Multiply (2 + x) * (2 + x)
1 + 2x + 4x2 = (2(2 + x) + x(2 + x))
1 + 2x + 4x2 = ((2 * 2 + x * 2) + x(2 + x))
1 + 2x + 4x2 = ((4 + 2x) + x(2 + x))
1 + 2x + 4x2 = (4 + 2x + (2 * x + x * x))
1 + 2x + 4x2 = (4 + 2x + (2x + x2))

Combine like terms: 2x + 2x = 4x
1 + 2x + 4x2 = (4 + 4x + x2)

Solving
1 + 2x + 4x2 = 4 + 4x + x2

Solving for variable 'x'.

Reorder the terms:
1 + -4 + 2x + -4x + 4x2 + -1x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Combine like terms: 1 + -4 = -3
-3 + 2x + -4x + 4x2 + -1x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Combine like terms: 2x + -4x = -2x
-3 + -2x + 4x2 + -1x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Combine like terms: 4x2 + -1x2 = 3x2
-3 + -2x + 3x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Reorder the terms:
-3 + -2x + 3x2 = 4 + -4 + 4x + -4x + x2 + -1x2

Combine like terms: 4 + -4 = 0
-3 + -2x + 3x2 = 0 + 4x + -4x + x2 + -1x2
-3 + -2x + 3x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
-3 + -2x + 3x2 = 0 + x2 + -1x2
-3 + -2x + 3x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-3 + -2x + 3x2 = 0

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

Divide each side by '3'.
-1 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.6666666667x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -0.6666666667x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.6666666667x + x2 = 0 + 1
-0.6666666667x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-0.6666666667x + x2 = 1

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = 1 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 1 + 0.1111111112

Combine like terms: 1 + 0.1111111112 = 1.1111111112
0.1111111112 + -0.6666666667x + x2 = 1.1111111112

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 1.1111111112

Calculate the square root of the right side: 1.054092553

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 1.054092553 and -1.054092553.


Subproblem 1
x + -0.3333333334 = 1.054092553

Simplifying
x + -0.3333333334 = 1.054092553

Reorder the terms:
-0.3333333334 + x = 1.054092553

Solving
-0.3333333334 + x = 1.054092553

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = 1.054092553 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = 1.054092553 + 0.3333333334
x = 1.054092553 + 0.3333333334

Combine like terms: 1.054092553 + 0.3333333334 = 1.3874258864
x = 1.3874258864

Simplifying
x = 1.3874258864


Subproblem 2
x + -0.3333333334 = -1.054092553

Simplifying
x + -0.3333333334 = -1.054092553

Reorder the terms:
-0.3333333334 + x = -1.054092553

Solving
-0.3333333334 + x = -1.054092553

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = -1.054092553 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = -1.054092553 + 0.3333333334
x = -1.054092553 + 0.3333333334

Combine like terms: -1.054092553 + 0.3333333334 = -0.7207592196
x = -0.7207592196

Simplifying
x = -0.7207592196


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.3874258864, -0.7207592196}

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