(2x-5)(x+4)=5

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Solution for (2x-5)(x+4)=5 equation: 


Simplifying
(2x + -5)(x + 4) = 5

Reorder the terms:
(-5 + 2x)(x + 4) = 5

Reorder the terms:
(-5 + 2x)(4 + x) = 5

Multiply (-5 + 2x) * (4 + x)
(-5(4 + x) + 2x * (4 + x)) = 5
((4 * -5 + x * -5) + 2x * (4 + x)) = 5
((-20 + -5x) + 2x * (4 + x)) = 5
(-20 + -5x + (4 * 2x + x * 2x)) = 5
(-20 + -5x + (8x + 2x2)) = 5

Combine like terms: -5x + 8x = 3x
(-20 + 3x + 2x2) = 5

Solving
-20 + 3x + 2x2 = 5

Solving for variable 'x'.

Reorder the terms:
-20 + -5 + 3x + 2x2 = 5 + -5

Combine like terms: -20 + -5 = -25
-25 + 3x + 2x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-25 + 3x + 2x2 = 0

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

Divide each side by '2'.
-12.5 + 1.5x + x2 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + 1.5x + 12.5 + x2 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + 1.5x + x2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + 1.5x + x2 = 0 + 12.5
1.5x + x2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
1.5x + x2 = 12.5

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 12.5 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 12.5 + 0.5625

Combine like terms: 12.5 + 0.5625 = 13.0625
0.5625 + 1.5x + x2 = 13.0625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 13.0625

Calculate the square root of the right side: 3.614208074

Break this problem into two subproblems by setting 
(x + 0.75) equal to 3.614208074 and -3.614208074.


Subproblem 1
x + 0.75 = 3.614208074

Simplifying
x + 0.75 = 3.614208074

Reorder the terms:
0.75 + x = 3.614208074

Solving
0.75 + x = 3.614208074

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 3.614208074 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 3.614208074 + -0.75
x = 3.614208074 + -0.75

Combine like terms: 3.614208074 + -0.75 = 2.864208074
x = 2.864208074

Simplifying
x = 2.864208074


Subproblem 2
x + 0.75 = -3.614208074

Simplifying
x + 0.75 = -3.614208074

Reorder the terms:
0.75 + x = -3.614208074

Solving
0.75 + x = -3.614208074

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -3.614208074 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -3.614208074 + -0.75
x = -3.614208074 + -0.75

Combine like terms: -3.614208074 + -0.75 = -4.364208074
x = -4.364208074

Simplifying
x = -4.364208074


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.864208074, -4.364208074}

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