3(x-2)+2x(x+1)=

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Solution for 3(x-2)+2x(x+1)= equation:


Simplifying
3(x + -2) + 2x(x + 1) = 0

Reorder the terms:
3(-2 + x) + 2x(x + 1) = 0
(-2 * 3 + x * 3) + 2x(x + 1) = 0
(-6 + 3x) + 2x(x + 1) = 0

Reorder the terms:
-6 + 3x + 2x(1 + x) = 0
-6 + 3x + (1 * 2x + x * 2x) = 0
-6 + 3x + (2x + 2x2) = 0

Combine like terms: 3x + 2x = 5x
-6 + 5x + 2x2 = 0

Solving
-6 + 5x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-3 + 2.5x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 2.5x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 2.5x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2.5x + x2 = 0 + 3
2.5x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
2.5x + x2 = 3

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 3 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 3 + 1.5625

Combine like terms: 3 + 1.5625 = 4.5625
1.5625 + 2.5x + x2 = 4.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(x + 1.25) equal to 2.136000936 and -2.136000936.

Subproblem 1

x + 1.25 = 2.136000936 Simplifying x + 1.25 = 2.136000936 Reorder the terms: 1.25 + x = 2.136000936 Solving 1.25 + x = 2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 2.136000936 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 2.136000936 + -1.25 x = 2.136000936 + -1.25 Combine like terms: 2.136000936 + -1.25 = 0.886000936 x = 0.886000936 Simplifying x = 0.886000936

Subproblem 2

x + 1.25 = -2.136000936 Simplifying x + 1.25 = -2.136000936 Reorder the terms: 1.25 + x = -2.136000936 Solving 1.25 + x = -2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -2.136000936 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -2.136000936 + -1.25 x = -2.136000936 + -1.25 Combine like terms: -2.136000936 + -1.25 = -3.386000936 x = -3.386000936 Simplifying x = -3.386000936

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.886000936, -3.386000936}

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