(x+5)(x+2)=25

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Solution for (x+5)(x+2)=25 equation:


Simplifying
(x + 5)(x + 2) = 25

Reorder the terms:
(5 + x)(x + 2) = 25

Reorder the terms:
(5 + x)(2 + x) = 25

Multiply (5 + x) * (2 + x)
(5(2 + x) + x(2 + x)) = 25
((2 * 5 + x * 5) + x(2 + x)) = 25
((10 + 5x) + x(2 + x)) = 25
(10 + 5x + (2 * x + x * x)) = 25
(10 + 5x + (2x + x2)) = 25

Combine like terms: 5x + 2x = 7x
(10 + 7x + x2) = 25

Solving
10 + 7x + x2 = 25

Solving for variable 'x'.

Reorder the terms:
10 + -25 + 7x + x2 = 25 + -25

Combine like terms: 10 + -25 = -15
-15 + 7x + x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-15 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 7x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + 7x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 7x + x2 = 0 + 15
7x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
7x + x2 = 15

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 = 15 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 15 + 12.25

Combine like terms: 15 + 12.25 = 27.25
12.25 + 7x + x2 = 27.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(x + 3.5) equal to 5.220153254 and -5.220153254.

Subproblem 1

x + 3.5 = 5.220153254 Simplifying x + 3.5 = 5.220153254 Reorder the terms: 3.5 + x = 5.220153254 Solving 3.5 + x = 5.220153254 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 = 5.220153254 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 5.220153254 + -3.5 x = 5.220153254 + -3.5 Combine like terms: 5.220153254 + -3.5 = 1.720153254 x = 1.720153254 Simplifying x = 1.720153254

Subproblem 2

x + 3.5 = -5.220153254 Simplifying x + 3.5 = -5.220153254 Reorder the terms: 3.5 + x = -5.220153254 Solving 3.5 + x = -5.220153254 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 = -5.220153254 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -5.220153254 + -3.5 x = -5.220153254 + -3.5 Combine like terms: -5.220153254 + -3.5 = -8.720153254 x = -8.720153254 Simplifying x = -8.720153254

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.720153254, -8.720153254}

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