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

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Solution for x(x+4)+x(x+2)=2x*2x+1 equation:


Simplifying
x(x + 4) + x(x + 2) = 2x * 2x + 1

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

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

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

Combine like terms: 4x + 2x = 6x
6x + x2 + x2 = 2x * 2x + 1

Combine like terms: x2 + x2 = 2x2
6x + 2x2 = 2x * 2x + 1

Reorder the terms for easier multiplication:
6x + 2x2 = 2 * 2x * x + 1

Multiply 2 * 2
6x + 2x2 = 4x * x + 1

Multiply x * x
6x + 2x2 = 4x2 + 1

Reorder the terms:
6x + 2x2 = 1 + 4x2

Solving
6x + 2x2 = 1 + 4x2

Solving for variable 'x'.

Reorder the terms:
-1 + 6x + 2x2 + -4x2 = 1 + 4x2 + -1 + -4x2

Combine like terms: 2x2 + -4x2 = -2x2
-1 + 6x + -2x2 = 1 + 4x2 + -1 + -4x2

Reorder the terms:
-1 + 6x + -2x2 = 1 + -1 + 4x2 + -4x2

Combine like terms: 1 + -1 = 0
-1 + 6x + -2x2 = 0 + 4x2 + -4x2
-1 + 6x + -2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-1 + 6x + -2x2 = 0

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

Divide each side by '-2'.
0.5 + -3x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -3x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -3x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -3x + x2 = 0 + -0.5
-3x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-3x + x2 = -0.5

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -0.5 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -0.5 + 2.25

Combine like terms: -0.5 + 2.25 = 1.75
2.25 + -3x + x2 = 1.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.322875656 and -1.322875656.

Subproblem 1

x + -1.5 = 1.322875656 Simplifying x + -1.5 = 1.322875656 Reorder the terms: -1.5 + x = 1.322875656 Solving -1.5 + x = 1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.322875656 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.322875656 + 1.5 x = 1.322875656 + 1.5 Combine like terms: 1.322875656 + 1.5 = 2.822875656 x = 2.822875656 Simplifying x = 2.822875656

Subproblem 2

x + -1.5 = -1.322875656 Simplifying x + -1.5 = -1.322875656 Reorder the terms: -1.5 + x = -1.322875656 Solving -1.5 + x = -1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.322875656 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.322875656 + 1.5 x = -1.322875656 + 1.5 Combine like terms: -1.322875656 + 1.5 = 0.177124344 x = 0.177124344 Simplifying x = 0.177124344

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.822875656, 0.177124344}

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