2x(4x+8)=3x-4

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Solution for 2x(4x+8)=3x-4 equation:


Simplifying
2x(4x + 8) = 3x + -4

Reorder the terms:
2x(8 + 4x) = 3x + -4
(8 * 2x + 4x * 2x) = 3x + -4
(16x + 8x2) = 3x + -4

Reorder the terms:
16x + 8x2 = -4 + 3x

Solving
16x + 8x2 = -4 + 3x

Solving for variable 'x'.

Reorder the terms:
4 + 16x + -3x + 8x2 = -4 + 3x + 4 + -3x

Combine like terms: 16x + -3x = 13x
4 + 13x + 8x2 = -4 + 3x + 4 + -3x

Reorder the terms:
4 + 13x + 8x2 = -4 + 4 + 3x + -3x

Combine like terms: -4 + 4 = 0
4 + 13x + 8x2 = 0 + 3x + -3x
4 + 13x + 8x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
4 + 13x + 8x2 = 0

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

Divide each side by '8'.
0.5 + 1.625x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 1.625x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 1.625x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 1.625x + x2 = 0 + -0.5
1.625x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
1.625x + x2 = -0.5

The x term is 1.625x.  Take half its coefficient (0.8125).
Square it (0.66015625) and add it to both sides.

Add '0.66015625' to each side of the equation.
1.625x + 0.66015625 + x2 = -0.5 + 0.66015625

Reorder the terms:
0.66015625 + 1.625x + x2 = -0.5 + 0.66015625

Combine like terms: -0.5 + 0.66015625 = 0.16015625
0.66015625 + 1.625x + x2 = 0.16015625

Factor a perfect square on the left side:
(x + 0.8125)(x + 0.8125) = 0.16015625

Calculate the square root of the right side: 0.400195265

Break this problem into two subproblems by setting 
(x + 0.8125) equal to 0.400195265 and -0.400195265.

Subproblem 1

x + 0.8125 = 0.400195265 Simplifying x + 0.8125 = 0.400195265 Reorder the terms: 0.8125 + x = 0.400195265 Solving 0.8125 + x = 0.400195265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8125' to each side of the equation. 0.8125 + -0.8125 + x = 0.400195265 + -0.8125 Combine like terms: 0.8125 + -0.8125 = 0.0000 0.0000 + x = 0.400195265 + -0.8125 x = 0.400195265 + -0.8125 Combine like terms: 0.400195265 + -0.8125 = -0.412304735 x = -0.412304735 Simplifying x = -0.412304735

Subproblem 2

x + 0.8125 = -0.400195265 Simplifying x + 0.8125 = -0.400195265 Reorder the terms: 0.8125 + x = -0.400195265 Solving 0.8125 + x = -0.400195265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8125' to each side of the equation. 0.8125 + -0.8125 + x = -0.400195265 + -0.8125 Combine like terms: 0.8125 + -0.8125 = 0.0000 0.0000 + x = -0.400195265 + -0.8125 x = -0.400195265 + -0.8125 Combine like terms: -0.400195265 + -0.8125 = -1.212695265 x = -1.212695265 Simplifying x = -1.212695265

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.412304735, -1.212695265}

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