(8x-1)*(5+2x)=(4x-5)2

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Solution for (8x-1)*(5+2x)=(4x-5)2 equation:


Simplifying
(8x + -1)(5 + 2x) = (4x + -5) * 2

Reorder the terms:
(-1 + 8x)(5 + 2x) = (4x + -5) * 2

Multiply (-1 + 8x) * (5 + 2x)
(-1(5 + 2x) + 8x * (5 + 2x)) = (4x + -5) * 2
((5 * -1 + 2x * -1) + 8x * (5 + 2x)) = (4x + -5) * 2
((-5 + -2x) + 8x * (5 + 2x)) = (4x + -5) * 2
(-5 + -2x + (5 * 8x + 2x * 8x)) = (4x + -5) * 2
(-5 + -2x + (40x + 16x2)) = (4x + -5) * 2

Combine like terms: -2x + 40x = 38x
(-5 + 38x + 16x2) = (4x + -5) * 2

Reorder the terms:
-5 + 38x + 16x2 = (-5 + 4x) * 2

Reorder the terms for easier multiplication:
-5 + 38x + 16x2 = 2(-5 + 4x)
-5 + 38x + 16x2 = (-5 * 2 + 4x * 2)
-5 + 38x + 16x2 = (-10 + 8x)

Solving
-5 + 38x + 16x2 = -10 + 8x

Solving for variable 'x'.

Reorder the terms:
-5 + 10 + 38x + -8x + 16x2 = -10 + 8x + 10 + -8x

Combine like terms: -5 + 10 = 5
5 + 38x + -8x + 16x2 = -10 + 8x + 10 + -8x

Combine like terms: 38x + -8x = 30x
5 + 30x + 16x2 = -10 + 8x + 10 + -8x

Reorder the terms:
5 + 30x + 16x2 = -10 + 10 + 8x + -8x

Combine like terms: -10 + 10 = 0
5 + 30x + 16x2 = 0 + 8x + -8x
5 + 30x + 16x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
5 + 30x + 16x2 = 0

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

Divide each side by '16'.
0.3125 + 1.875x + x2 = 0

Move the constant term to the right:

Add '-0.3125' to each side of the equation.
0.3125 + 1.875x + -0.3125 + x2 = 0 + -0.3125

Reorder the terms:
0.3125 + -0.3125 + 1.875x + x2 = 0 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + 1.875x + x2 = 0 + -0.3125
1.875x + x2 = 0 + -0.3125

Combine like terms: 0 + -0.3125 = -0.3125
1.875x + x2 = -0.3125

The x term is 1.875x.  Take half its coefficient (0.9375).
Square it (0.87890625) and add it to both sides.

Add '0.87890625' to each side of the equation.
1.875x + 0.87890625 + x2 = -0.3125 + 0.87890625

Reorder the terms:
0.87890625 + 1.875x + x2 = -0.3125 + 0.87890625

Combine like terms: -0.3125 + 0.87890625 = 0.56640625
0.87890625 + 1.875x + x2 = 0.56640625

Factor a perfect square on the left side:
(x + 0.9375)(x + 0.9375) = 0.56640625

Calculate the square root of the right side: 0.752599661

Break this problem into two subproblems by setting 
(x + 0.9375) equal to 0.752599661 and -0.752599661.

Subproblem 1

x + 0.9375 = 0.752599661 Simplifying x + 0.9375 = 0.752599661 Reorder the terms: 0.9375 + x = 0.752599661 Solving 0.9375 + x = 0.752599661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + x = 0.752599661 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + x = 0.752599661 + -0.9375 x = 0.752599661 + -0.9375 Combine like terms: 0.752599661 + -0.9375 = -0.184900339 x = -0.184900339 Simplifying x = -0.184900339

Subproblem 2

x + 0.9375 = -0.752599661 Simplifying x + 0.9375 = -0.752599661 Reorder the terms: 0.9375 + x = -0.752599661 Solving 0.9375 + x = -0.752599661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + x = -0.752599661 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + x = -0.752599661 + -0.9375 x = -0.752599661 + -0.9375 Combine like terms: -0.752599661 + -0.9375 = -1.690099661 x = -1.690099661 Simplifying x = -1.690099661

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.184900339, -1.690099661}

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