5x(2x+1)=4-4x

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Solution for 5x(2x+1)=4-4x equation:


Simplifying
5x(2x + 1) = 4 + -4x

Reorder the terms:
5x(1 + 2x) = 4 + -4x
(1 * 5x + 2x * 5x) = 4 + -4x
(5x + 10x2) = 4 + -4x

Solving
5x + 10x2 = 4 + -4x

Solving for variable 'x'.

Reorder the terms:
-4 + 5x + 4x + 10x2 = 4 + -4x + -4 + 4x

Combine like terms: 5x + 4x = 9x
-4 + 9x + 10x2 = 4 + -4x + -4 + 4x

Reorder the terms:
-4 + 9x + 10x2 = 4 + -4 + -4x + 4x

Combine like terms: 4 + -4 = 0
-4 + 9x + 10x2 = 0 + -4x + 4x
-4 + 9x + 10x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-4 + 9x + 10x2 = 0

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

Divide each side by '10'.
-0.4 + 0.9x + x2 = 0.0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 0.9x + 0.4 + x2 = 0.0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 0.9x + x2 = 0.0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 0.9x + x2 = 0.0 + 0.4
0.9x + x2 = 0.0 + 0.4

Combine like terms: 0.0 + 0.4 = 0.4
0.9x + x2 = 0.4

The x term is 0.9x.  Take half its coefficient (0.45).
Square it (0.2025) and add it to both sides.

Add '0.2025' to each side of the equation.
0.9x + 0.2025 + x2 = 0.4 + 0.2025

Reorder the terms:
0.2025 + 0.9x + x2 = 0.4 + 0.2025

Combine like terms: 0.4 + 0.2025 = 0.6025
0.2025 + 0.9x + x2 = 0.6025

Factor a perfect square on the left side:
(x + 0.45)(x + 0.45) = 0.6025

Calculate the square root of the right side: 0.776208735

Break this problem into two subproblems by setting 
(x + 0.45) equal to 0.776208735 and -0.776208735.

Subproblem 1

x + 0.45 = 0.776208735 Simplifying x + 0.45 = 0.776208735 Reorder the terms: 0.45 + x = 0.776208735 Solving 0.45 + x = 0.776208735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + x = 0.776208735 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = 0.776208735 + -0.45 x = 0.776208735 + -0.45 Combine like terms: 0.776208735 + -0.45 = 0.326208735 x = 0.326208735 Simplifying x = 0.326208735

Subproblem 2

x + 0.45 = -0.776208735 Simplifying x + 0.45 = -0.776208735 Reorder the terms: 0.45 + x = -0.776208735 Solving 0.45 + x = -0.776208735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + x = -0.776208735 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = -0.776208735 + -0.45 x = -0.776208735 + -0.45 Combine like terms: -0.776208735 + -0.45 = -1.226208735 x = -1.226208735 Simplifying x = -1.226208735

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.326208735, -1.226208735}

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