8x-3+5x(2+x)=0

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Solution for 8x-3+5x(2+x)=0 equation:


Simplifying
8x + -3 + 5x(2 + x) = 0
8x + -3 + (2 * 5x + x * 5x) = 0
8x + -3 + (10x + 5x2) = 0

Reorder the terms:
-3 + 8x + 10x + 5x2 = 0

Combine like terms: 8x + 10x = 18x
-3 + 18x + 5x2 = 0

Solving
-3 + 18x + 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'.
-0.6 + 3.6x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 3.6x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 3.6x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 3.6x + x2 = 0 + 0.6
3.6x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
3.6x + x2 = 0.6

The x term is 3.6x.  Take half its coefficient (1.8).
Square it (3.24) and add it to both sides.

Add '3.24' to each side of the equation.
3.6x + 3.24 + x2 = 0.6 + 3.24

Reorder the terms:
3.24 + 3.6x + x2 = 0.6 + 3.24

Combine like terms: 0.6 + 3.24 = 3.84
3.24 + 3.6x + x2 = 3.84

Factor a perfect square on the left side:
(x + 1.8)(x + 1.8) = 3.84

Calculate the square root of the right side: 1.959591794

Break this problem into two subproblems by setting 
(x + 1.8) equal to 1.959591794 and -1.959591794.

Subproblem 1

x + 1.8 = 1.959591794 Simplifying x + 1.8 = 1.959591794 Reorder the terms: 1.8 + x = 1.959591794 Solving 1.8 + x = 1.959591794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = 1.959591794 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = 1.959591794 + -1.8 x = 1.959591794 + -1.8 Combine like terms: 1.959591794 + -1.8 = 0.159591794 x = 0.159591794 Simplifying x = 0.159591794

Subproblem 2

x + 1.8 = -1.959591794 Simplifying x + 1.8 = -1.959591794 Reorder the terms: 1.8 + x = -1.959591794 Solving 1.8 + x = -1.959591794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = -1.959591794 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = -1.959591794 + -1.8 x = -1.959591794 + -1.8 Combine like terms: -1.959591794 + -1.8 = -3.759591794 x = -3.759591794 Simplifying x = -3.759591794

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.159591794, -3.759591794}

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