(2x+3)(x+1)=18

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Solution for (2x+3)(x+1)=18 equation:


Simplifying
(2x + 3)(x + 1) = 18

Reorder the terms:
(3 + 2x)(x + 1) = 18

Reorder the terms:
(3 + 2x)(1 + x) = 18

Multiply (3 + 2x) * (1 + x)
(3(1 + x) + 2x * (1 + x)) = 18
((1 * 3 + x * 3) + 2x * (1 + x)) = 18
((3 + 3x) + 2x * (1 + x)) = 18
(3 + 3x + (1 * 2x + x * 2x)) = 18
(3 + 3x + (2x + 2x2)) = 18

Combine like terms: 3x + 2x = 5x
(3 + 5x + 2x2) = 18

Solving
3 + 5x + 2x2 = 18

Solving for variable 'x'.

Reorder the terms:
3 + -18 + 5x + 2x2 = 18 + -18

Combine like terms: 3 + -18 = -15
-15 + 5x + 2x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-15 + 5x + 2x2 = 0

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

Divide each side by '2'.
-7.5 + 2.5x + x2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + 2.5x + 7.5 + x2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + 2.5x + x2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + 2.5x + x2 = 0 + 7.5
2.5x + x2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
2.5x + x2 = 7.5

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 = 7.5 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 7.5 + 1.5625

Combine like terms: 7.5 + 1.5625 = 9.0625
1.5625 + 2.5x + x2 = 9.0625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 9.0625

Calculate the square root of the right side: 3.010398645

Break this problem into two subproblems by setting 
(x + 1.25) equal to 3.010398645 and -3.010398645.

Subproblem 1

x + 1.25 = 3.010398645 Simplifying x + 1.25 = 3.010398645 Reorder the terms: 1.25 + x = 3.010398645 Solving 1.25 + x = 3.010398645 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 = 3.010398645 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 3.010398645 + -1.25 x = 3.010398645 + -1.25 Combine like terms: 3.010398645 + -1.25 = 1.760398645 x = 1.760398645 Simplifying x = 1.760398645

Subproblem 2

x + 1.25 = -3.010398645 Simplifying x + 1.25 = -3.010398645 Reorder the terms: 1.25 + x = -3.010398645 Solving 1.25 + x = -3.010398645 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 = -3.010398645 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -3.010398645 + -1.25 x = -3.010398645 + -1.25 Combine like terms: -3.010398645 + -1.25 = -4.260398645 x = -4.260398645 Simplifying x = -4.260398645

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.760398645, -4.260398645}

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