(2x+3)5x+2=

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


Simplifying
(2x + 3) * 5x + 2 = 0

Reorder the terms:
(3 + 2x) * 5x + 2 = 0

Reorder the terms for easier multiplication:
5x(3 + 2x) + 2 = 0
(3 * 5x + 2x * 5x) + 2 = 0
(15x + 10x2) + 2 = 0

Reorder the terms:
2 + 15x + 10x2 = 0

Solving
2 + 15x + 10x2 = 0

Solving for variable 'x'.

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

Divide each side by '10'.
0.2 + 1.5x + x2 = 0.0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 1.5x + -0.2 + x2 = 0.0 + -0.2

Reorder the terms:
0.2 + -0.2 + 1.5x + x2 = 0.0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 1.5x + x2 = 0.0 + -0.2
1.5x + x2 = 0.0 + -0.2

Combine like terms: 0.0 + -0.2 = -0.2
1.5x + x2 = -0.2

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = -0.2 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = -0.2 + 0.5625

Combine like terms: -0.2 + 0.5625 = 0.3625
0.5625 + 1.5x + x2 = 0.3625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 0.3625

Calculate the square root of the right side: 0.602079729

Break this problem into two subproblems by setting 
(x + 0.75) equal to 0.602079729 and -0.602079729.

Subproblem 1

x + 0.75 = 0.602079729 Simplifying x + 0.75 = 0.602079729 Reorder the terms: 0.75 + x = 0.602079729 Solving 0.75 + x = 0.602079729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 0.602079729 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 0.602079729 + -0.75 x = 0.602079729 + -0.75 Combine like terms: 0.602079729 + -0.75 = -0.147920271 x = -0.147920271 Simplifying x = -0.147920271

Subproblem 2

x + 0.75 = -0.602079729 Simplifying x + 0.75 = -0.602079729 Reorder the terms: 0.75 + x = -0.602079729 Solving 0.75 + x = -0.602079729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -0.602079729 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -0.602079729 + -0.75 x = -0.602079729 + -0.75 Combine like terms: -0.602079729 + -0.75 = -1.352079729 x = -1.352079729 Simplifying x = -1.352079729

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.147920271, -1.352079729}

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