2x(x+4)=2x+5

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Solution for 2x(x+4)=2x+5 equation:


Simplifying
2x(x + 4) = 2x + 5

Reorder the terms:
2x(4 + x) = 2x + 5
(4 * 2x + x * 2x) = 2x + 5
(8x + 2x2) = 2x + 5

Reorder the terms:
8x + 2x2 = 5 + 2x

Solving
8x + 2x2 = 5 + 2x

Solving for variable 'x'.

Reorder the terms:
-5 + 8x + -2x + 2x2 = 5 + 2x + -5 + -2x

Combine like terms: 8x + -2x = 6x
-5 + 6x + 2x2 = 5 + 2x + -5 + -2x

Reorder the terms:
-5 + 6x + 2x2 = 5 + -5 + 2x + -2x

Combine like terms: 5 + -5 = 0
-5 + 6x + 2x2 = 0 + 2x + -2x
-5 + 6x + 2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-5 + 6x + 2x2 = 0

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

Divide each side by '2'.
-2.5 + 3x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 3x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 3x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 3x + x2 = 0 + 2.5
3x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
3x + x2 = 2.5

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 = 2.5 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 2.5 + 2.25

Combine like terms: 2.5 + 2.25 = 4.75
2.25 + 3x + x2 = 4.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 4.75

Calculate the square root of the right side: 2.179449472

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2.179449472 and -2.179449472.

Subproblem 1

x + 1.5 = 2.179449472 Simplifying x + 1.5 = 2.179449472 Reorder the terms: 1.5 + x = 2.179449472 Solving 1.5 + x = 2.179449472 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 = 2.179449472 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.179449472 + -1.5 x = 2.179449472 + -1.5 Combine like terms: 2.179449472 + -1.5 = 0.679449472 x = 0.679449472 Simplifying x = 0.679449472

Subproblem 2

x + 1.5 = -2.179449472 Simplifying x + 1.5 = -2.179449472 Reorder the terms: 1.5 + x = -2.179449472 Solving 1.5 + x = -2.179449472 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 = -2.179449472 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.179449472 + -1.5 x = -2.179449472 + -1.5 Combine like terms: -2.179449472 + -1.5 = -3.679449472 x = -3.679449472 Simplifying x = -3.679449472

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.679449472, -3.679449472}

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