(x+5)(x+4)=36

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Solution for (x+5)(x+4)=36 equation:


Simplifying
(x + 5)(x + 4) = 36

Reorder the terms:
(5 + x)(x + 4) = 36

Reorder the terms:
(5 + x)(4 + x) = 36

Multiply (5 + x) * (4 + x)
(5(4 + x) + x(4 + x)) = 36
((4 * 5 + x * 5) + x(4 + x)) = 36
((20 + 5x) + x(4 + x)) = 36
(20 + 5x + (4 * x + x * x)) = 36
(20 + 5x + (4x + x2)) = 36

Combine like terms: 5x + 4x = 9x
(20 + 9x + x2) = 36

Solving
20 + 9x + x2 = 36

Solving for variable 'x'.

Reorder the terms:
20 + -36 + 9x + x2 = 36 + -36

Combine like terms: 20 + -36 = -16
-16 + 9x + x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-16 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 9x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 9x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 9x + x2 = 0 + 16
9x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
9x + x2 = 16

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 = 16 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 16 + 20.25

Combine like terms: 16 + 20.25 = 36.25
20.25 + 9x + x2 = 36.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(x + 4.5) equal to 6.020797289 and -6.020797289.

Subproblem 1

x + 4.5 = 6.020797289 Simplifying x + 4.5 = 6.020797289 Reorder the terms: 4.5 + x = 6.020797289 Solving 4.5 + x = 6.020797289 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 = 6.020797289 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 6.020797289 + -4.5 x = 6.020797289 + -4.5 Combine like terms: 6.020797289 + -4.5 = 1.520797289 x = 1.520797289 Simplifying x = 1.520797289

Subproblem 2

x + 4.5 = -6.020797289 Simplifying x + 4.5 = -6.020797289 Reorder the terms: 4.5 + x = -6.020797289 Solving 4.5 + x = -6.020797289 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 = -6.020797289 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -6.020797289 + -4.5 x = -6.020797289 + -4.5 Combine like terms: -6.020797289 + -4.5 = -10.520797289 x = -10.520797289 Simplifying x = -10.520797289

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.520797289, -10.520797289}

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