(2x+5)(2x+1)=180

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Solution for (2x+5)(2x+1)=180 equation:


Simplifying
(2x + 5)(2x + 1) = 180

Reorder the terms:
(5 + 2x)(2x + 1) = 180

Reorder the terms:
(5 + 2x)(1 + 2x) = 180

Multiply (5 + 2x) * (1 + 2x)
(5(1 + 2x) + 2x * (1 + 2x)) = 180
((1 * 5 + 2x * 5) + 2x * (1 + 2x)) = 180
((5 + 10x) + 2x * (1 + 2x)) = 180
(5 + 10x + (1 * 2x + 2x * 2x)) = 180
(5 + 10x + (2x + 4x2)) = 180

Combine like terms: 10x + 2x = 12x
(5 + 12x + 4x2) = 180

Solving
5 + 12x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
5 + -180 + 12x + 4x2 = 180 + -180

Combine like terms: 5 + -180 = -175
-175 + 12x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-175 + 12x + 4x2 = 0

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

Divide each side by '4'.
-43.75 + 3x + x2 = 0

Move the constant term to the right:

Add '43.75' to each side of the equation.
-43.75 + 3x + 43.75 + x2 = 0 + 43.75

Reorder the terms:
-43.75 + 43.75 + 3x + x2 = 0 + 43.75

Combine like terms: -43.75 + 43.75 = 0.00
0.00 + 3x + x2 = 0 + 43.75
3x + x2 = 0 + 43.75

Combine like terms: 0 + 43.75 = 43.75
3x + x2 = 43.75

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 43.75 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 43.75 + 2.25

Combine like terms: 43.75 + 2.25 = 46
2.25 + 3x + x2 = 46

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(x + 1.5) equal to 6.782329983 and -6.782329983.

Subproblem 1

x + 1.5 = 6.782329983 Simplifying x + 1.5 = 6.782329983 Reorder the terms: 1.5 + x = 6.782329983 Solving 1.5 + x = 6.782329983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 6.782329983 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 6.782329983 + -1.5 x = 6.782329983 + -1.5 Combine like terms: 6.782329983 + -1.5 = 5.282329983 x = 5.282329983 Simplifying x = 5.282329983

Subproblem 2

x + 1.5 = -6.782329983 Simplifying x + 1.5 = -6.782329983 Reorder the terms: 1.5 + x = -6.782329983 Solving 1.5 + x = -6.782329983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -6.782329983 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -6.782329983 + -1.5 x = -6.782329983 + -1.5 Combine like terms: -6.782329983 + -1.5 = -8.282329983 x = -8.282329983 Simplifying x = -8.282329983

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.282329983, -8.282329983}

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