(2x+5)(x+1)=52

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Solution for (2x+5)(x+1)=52 equation:


Simplifying
(2x + 5)(x + 1) = 52

Reorder the terms:
(5 + 2x)(x + 1) = 52

Reorder the terms:
(5 + 2x)(1 + x) = 52

Multiply (5 + 2x) * (1 + x)
(5(1 + x) + 2x * (1 + x)) = 52
((1 * 5 + x * 5) + 2x * (1 + x)) = 52
((5 + 5x) + 2x * (1 + x)) = 52
(5 + 5x + (1 * 2x + x * 2x)) = 52
(5 + 5x + (2x + 2x2)) = 52

Combine like terms: 5x + 2x = 7x
(5 + 7x + 2x2) = 52

Solving
5 + 7x + 2x2 = 52

Solving for variable 'x'.

Reorder the terms:
5 + -52 + 7x + 2x2 = 52 + -52

Combine like terms: 5 + -52 = -47
-47 + 7x + 2x2 = 52 + -52

Combine like terms: 52 + -52 = 0
-47 + 7x + 2x2 = 0

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

Divide each side by '2'.
-23.5 + 3.5x + x2 = 0

Move the constant term to the right:

Add '23.5' to each side of the equation.
-23.5 + 3.5x + 23.5 + x2 = 0 + 23.5

Reorder the terms:
-23.5 + 23.5 + 3.5x + x2 = 0 + 23.5

Combine like terms: -23.5 + 23.5 = 0.0
0.0 + 3.5x + x2 = 0 + 23.5
3.5x + x2 = 0 + 23.5

Combine like terms: 0 + 23.5 = 23.5
3.5x + x2 = 23.5

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 23.5 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 23.5 + 3.0625

Combine like terms: 23.5 + 3.0625 = 26.5625
3.0625 + 3.5x + x2 = 26.5625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 26.5625

Calculate the square root of the right side: 5.153882032

Break this problem into two subproblems by setting 
(x + 1.75) equal to 5.153882032 and -5.153882032.

Subproblem 1

x + 1.75 = 5.153882032 Simplifying x + 1.75 = 5.153882032 Reorder the terms: 1.75 + x = 5.153882032 Solving 1.75 + x = 5.153882032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 5.153882032 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 5.153882032 + -1.75 x = 5.153882032 + -1.75 Combine like terms: 5.153882032 + -1.75 = 3.403882032 x = 3.403882032 Simplifying x = 3.403882032

Subproblem 2

x + 1.75 = -5.153882032 Simplifying x + 1.75 = -5.153882032 Reorder the terms: 1.75 + x = -5.153882032 Solving 1.75 + x = -5.153882032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -5.153882032 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -5.153882032 + -1.75 x = -5.153882032 + -1.75 Combine like terms: -5.153882032 + -1.75 = -6.903882032 x = -6.903882032 Simplifying x = -6.903882032

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.403882032, -6.903882032}

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