(2x+5)(x+2)=54

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Solution for (2x+5)(x+2)=54 equation:


Simplifying
(2x + 5)(x + 2) = 54

Reorder the terms:
(5 + 2x)(x + 2) = 54

Reorder the terms:
(5 + 2x)(2 + x) = 54

Multiply (5 + 2x) * (2 + x)
(5(2 + x) + 2x * (2 + x)) = 54
((2 * 5 + x * 5) + 2x * (2 + x)) = 54
((10 + 5x) + 2x * (2 + x)) = 54
(10 + 5x + (2 * 2x + x * 2x)) = 54
(10 + 5x + (4x + 2x2)) = 54

Combine like terms: 5x + 4x = 9x
(10 + 9x + 2x2) = 54

Solving
10 + 9x + 2x2 = 54

Solving for variable 'x'.

Reorder the terms:
10 + -54 + 9x + 2x2 = 54 + -54

Combine like terms: 10 + -54 = -44
-44 + 9x + 2x2 = 54 + -54

Combine like terms: 54 + -54 = 0
-44 + 9x + 2x2 = 0

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

Divide each side by '2'.
-22 + 4.5x + x2 = 0

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + 4.5x + 22 + x2 = 0 + 22

Reorder the terms:
-22 + 22 + 4.5x + x2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + 4.5x + x2 = 0 + 22
4.5x + x2 = 0 + 22

Combine like terms: 0 + 22 = 22
4.5x + x2 = 22

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = 22 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = 22 + 5.0625

Combine like terms: 22 + 5.0625 = 27.0625
5.0625 + 4.5x + x2 = 27.0625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 27.0625

Calculate the square root of the right side: 5.202163012

Break this problem into two subproblems by setting 
(x + 2.25) equal to 5.202163012 and -5.202163012.

Subproblem 1

x + 2.25 = 5.202163012 Simplifying x + 2.25 = 5.202163012 Reorder the terms: 2.25 + x = 5.202163012 Solving 2.25 + x = 5.202163012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 5.202163012 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 5.202163012 + -2.25 x = 5.202163012 + -2.25 Combine like terms: 5.202163012 + -2.25 = 2.952163012 x = 2.952163012 Simplifying x = 2.952163012

Subproblem 2

x + 2.25 = -5.202163012 Simplifying x + 2.25 = -5.202163012 Reorder the terms: 2.25 + x = -5.202163012 Solving 2.25 + x = -5.202163012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -5.202163012 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -5.202163012 + -2.25 x = -5.202163012 + -2.25 Combine like terms: -5.202163012 + -2.25 = -7.452163012 x = -7.452163012 Simplifying x = -7.452163012

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.952163012, -7.452163012}

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