(-5x+4)(x+2)+2x=0

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Solution for (-5x+4)(x+2)+2x=0 equation:


Simplifying
(-5x + 4)(x + 2) + 2x = 0

Reorder the terms:
(4 + -5x)(x + 2) + 2x = 0

Reorder the terms:
(4 + -5x)(2 + x) + 2x = 0

Multiply (4 + -5x) * (2 + x)
(4(2 + x) + -5x * (2 + x)) + 2x = 0
((2 * 4 + x * 4) + -5x * (2 + x)) + 2x = 0
((8 + 4x) + -5x * (2 + x)) + 2x = 0
(8 + 4x + (2 * -5x + x * -5x)) + 2x = 0
(8 + 4x + (-10x + -5x2)) + 2x = 0

Combine like terms: 4x + -10x = -6x
(8 + -6x + -5x2) + 2x = 0

Reorder the terms:
8 + -6x + 2x + -5x2 = 0

Combine like terms: -6x + 2x = -4x
8 + -4x + -5x2 = 0

Solving
8 + -4x + -5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-1.6 + 0.8x + x2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 0.8x + 1.6 + x2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + 0.8x + x2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 0.8x + x2 = 0 + 1.6
0.8x + x2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
0.8x + x2 = 1.6

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = 1.6 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 1.6 + 0.16

Combine like terms: 1.6 + 0.16 = 1.76
0.16 + 0.8x + x2 = 1.76

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 1.76

Calculate the square root of the right side: 1.326649916

Break this problem into two subproblems by setting 
(x + 0.4) equal to 1.326649916 and -1.326649916.

Subproblem 1

x + 0.4 = 1.326649916 Simplifying x + 0.4 = 1.326649916 Reorder the terms: 0.4 + x = 1.326649916 Solving 0.4 + x = 1.326649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 1.326649916 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 1.326649916 + -0.4 x = 1.326649916 + -0.4 Combine like terms: 1.326649916 + -0.4 = 0.926649916 x = 0.926649916 Simplifying x = 0.926649916

Subproblem 2

x + 0.4 = -1.326649916 Simplifying x + 0.4 = -1.326649916 Reorder the terms: 0.4 + x = -1.326649916 Solving 0.4 + x = -1.326649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -1.326649916 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -1.326649916 + -0.4 x = -1.326649916 + -0.4 Combine like terms: -1.326649916 + -0.4 = -1.726649916 x = -1.726649916 Simplifying x = -1.726649916

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.926649916, -1.726649916}

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