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

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


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

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

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

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

Combine like terms: 2x + 5x = 7x
(10 + 7x + x2) = 5

Solving
10 + 7x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
10 + -5 + 7x + x2 = 5 + -5

Combine like terms: 10 + -5 = 5
5 + 7x + x2 = 5 + -5

Combine like terms: 5 + -5 = 0
5 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 7x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 7x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 7x + x2 = 0 + -5
7x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
7x + x2 = -5

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = -5 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -5 + 12.25

Combine like terms: -5 + 12.25 = 7.25
12.25 + 7x + x2 = 7.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(x + 3.5) equal to 2.692582404 and -2.692582404.

Subproblem 1

x + 3.5 = 2.692582404 Simplifying x + 3.5 = 2.692582404 Reorder the terms: 3.5 + x = 2.692582404 Solving 3.5 + x = 2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 2.692582404 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 2.692582404 + -3.5 x = 2.692582404 + -3.5 Combine like terms: 2.692582404 + -3.5 = -0.807417596 x = -0.807417596 Simplifying x = -0.807417596

Subproblem 2

x + 3.5 = -2.692582404 Simplifying x + 3.5 = -2.692582404 Reorder the terms: 3.5 + x = -2.692582404 Solving 3.5 + x = -2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -2.692582404 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -2.692582404 + -3.5 x = -2.692582404 + -3.5 Combine like terms: -2.692582404 + -3.5 = -6.192582404 x = -6.192582404 Simplifying x = -6.192582404

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.807417596, -6.192582404}

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