(x+5)(x+4)=25

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Solution for (x+5)(x+4)=25 equation: 


Simplifying
(x + 5)(x + 4) = 25

Reorder the terms:
(5 + x)(x + 4) = 25

Reorder the terms:
(5 + x)(4 + x) = 25

Multiply (5 + x) * (4 + x)
(5(4 + x) + x(4 + x)) = 25
((4 * 5 + x * 5) + x(4 + x)) = 25
((20 + 5x) + x(4 + x)) = 25
(20 + 5x + (4 * x + x * x)) = 25
(20 + 5x + (4x + x2)) = 25

Combine like terms: 5x + 4x = 9x
(20 + 9x + x2) = 25

Solving
20 + 9x + x2 = 25

Solving for variable 'x'.

Reorder the terms:
20 + -25 + 9x + x2 = 25 + -25

Combine like terms: 20 + -25 = -5
-5 + 9x + x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-5 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 9x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 9x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 9x + x2 = 0 + 5
9x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
9x + x2 = 5

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 5 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 5 + 20.25

Combine like terms: 5 + 20.25 = 25.25
20.25 + 9x + x2 = 25.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 25.25

Calculate the square root of the right side: 5.024937811

Break this problem into two subproblems by setting 
(x + 4.5) equal to 5.024937811 and -5.024937811.


Subproblem 1
x + 4.5 = 5.024937811

Simplifying
x + 4.5 = 5.024937811

Reorder the terms:
4.5 + x = 5.024937811

Solving
4.5 + x = 5.024937811

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 5.024937811 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 5.024937811 + -4.5
x = 5.024937811 + -4.5

Combine like terms: 5.024937811 + -4.5 = 0.524937811
x = 0.524937811

Simplifying
x = 0.524937811


Subproblem 2
x + 4.5 = -5.024937811

Simplifying
x + 4.5 = -5.024937811

Reorder the terms:
4.5 + x = -5.024937811

Solving
4.5 + x = -5.024937811

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -5.024937811 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -5.024937811 + -4.5
x = -5.024937811 + -4.5

Combine like terms: -5.024937811 + -4.5 = -9.524937811
x = -9.524937811

Simplifying
x = -9.524937811


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.524937811, -9.524937811}

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