8x(2x+5)=3x-5

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Solution for 8x(2x+5)=3x-5 equation:


Simplifying
8x(2x + 5) = 3x + -5

Reorder the terms:
8x(5 + 2x) = 3x + -5
(5 * 8x + 2x * 8x) = 3x + -5
(40x + 16x2) = 3x + -5

Reorder the terms:
40x + 16x2 = -5 + 3x

Solving
40x + 16x2 = -5 + 3x

Solving for variable 'x'.

Reorder the terms:
5 + 40x + -3x + 16x2 = -5 + 3x + 5 + -3x

Combine like terms: 40x + -3x = 37x
5 + 37x + 16x2 = -5 + 3x + 5 + -3x

Reorder the terms:
5 + 37x + 16x2 = -5 + 5 + 3x + -3x

Combine like terms: -5 + 5 = 0
5 + 37x + 16x2 = 0 + 3x + -3x
5 + 37x + 16x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
5 + 37x + 16x2 = 0

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

Divide each side by '16'.
0.3125 + 2.3125x + x2 = 0

Move the constant term to the right:

Add '-0.3125' to each side of the equation.
0.3125 + 2.3125x + -0.3125 + x2 = 0 + -0.3125

Reorder the terms:
0.3125 + -0.3125 + 2.3125x + x2 = 0 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + 2.3125x + x2 = 0 + -0.3125
2.3125x + x2 = 0 + -0.3125

Combine like terms: 0 + -0.3125 = -0.3125
2.3125x + x2 = -0.3125

The x term is 2.3125x.  Take half its coefficient (1.15625).
Square it (1.336914063) and add it to both sides.

Add '1.336914063' to each side of the equation.
2.3125x + 1.336914063 + x2 = -0.3125 + 1.336914063

Reorder the terms:
1.336914063 + 2.3125x + x2 = -0.3125 + 1.336914063

Combine like terms: -0.3125 + 1.336914063 = 1.024414063
1.336914063 + 2.3125x + x2 = 1.024414063

Factor a perfect square on the left side:
(x + 1.15625)(x + 1.15625) = 1.024414063

Calculate the square root of the right side: 1.012133422

Break this problem into two subproblems by setting 
(x + 1.15625) equal to 1.012133422 and -1.012133422.

Subproblem 1

x + 1.15625 = 1.012133422 Simplifying x + 1.15625 = 1.012133422 Reorder the terms: 1.15625 + x = 1.012133422 Solving 1.15625 + x = 1.012133422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.15625' to each side of the equation. 1.15625 + -1.15625 + x = 1.012133422 + -1.15625 Combine like terms: 1.15625 + -1.15625 = 0.00000 0.00000 + x = 1.012133422 + -1.15625 x = 1.012133422 + -1.15625 Combine like terms: 1.012133422 + -1.15625 = -0.144116578 x = -0.144116578 Simplifying x = -0.144116578

Subproblem 2

x + 1.15625 = -1.012133422 Simplifying x + 1.15625 = -1.012133422 Reorder the terms: 1.15625 + x = -1.012133422 Solving 1.15625 + x = -1.012133422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.15625' to each side of the equation. 1.15625 + -1.15625 + x = -1.012133422 + -1.15625 Combine like terms: 1.15625 + -1.15625 = 0.00000 0.00000 + x = -1.012133422 + -1.15625 x = -1.012133422 + -1.15625 Combine like terms: -1.012133422 + -1.15625 = -2.168383422 x = -2.168383422 Simplifying x = -2.168383422

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.144116578, -2.168383422}

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