2x(x+4)=1

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


Simplifying
2x(x + 4) = 1

Reorder the terms:
2x(4 + x) = 1
(4 * 2x + x * 2x) = 1
(8x + 2x2) = 1

Solving
8x + 2x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + 8x + 2x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 8x + 2x2 = 0

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

Divide each side by '2'.
-0.5 + 4x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 4x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 4x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 4x + x2 = 0 + 0.5
4x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
4x + x2 = 0.5

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 = 0.5 + 4

Reorder the terms:
4 + 4x + x2 = 0.5 + 4

Combine like terms: 0.5 + 4 = 4.5
4 + 4x + x2 = 4.5

Factor a perfect square on the left side:
(x + 2)(x + 2) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(x + 2) equal to 2.121320344 and -2.121320344.

Subproblem 1

x + 2 = 2.121320344 Simplifying x + 2 = 2.121320344 Reorder the terms: 2 + x = 2.121320344 Solving 2 + x = 2.121320344 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 = 2.121320344 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.121320344 + -2 x = 2.121320344 + -2 Combine like terms: 2.121320344 + -2 = 0.121320344 x = 0.121320344 Simplifying x = 0.121320344

Subproblem 2

x + 2 = -2.121320344 Simplifying x + 2 = -2.121320344 Reorder the terms: 2 + x = -2.121320344 Solving 2 + x = -2.121320344 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 = -2.121320344 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.121320344 + -2 x = -2.121320344 + -2 Combine like terms: -2.121320344 + -2 = -4.121320344 x = -4.121320344 Simplifying x = -4.121320344

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.121320344, -4.121320344}

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