(3.8+x)(2.5+x)=78.25

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Solution for (3.8+x)(2.5+x)=78.25 equation: 


Simplifying
(3.8 + x)(2.5 + x) = 78.25

Multiply (3.8 + x) * (2.5 + x)
(3.8(2.5 + x) + x(2.5 + x)) = 78.25
((2.5 * 3.8 + x * 3.8) + x(2.5 + x)) = 78.25
((9.5 + 3.8x) + x(2.5 + x)) = 78.25
(9.5 + 3.8x + (2.5 * x + x * x)) = 78.25
(9.5 + 3.8x + (2.5x + x2)) = 78.25

Combine like terms: 3.8x + 2.5x = 6.3x
(9.5 + 6.3x + x2) = 78.25

Solving
9.5 + 6.3x + x2 = 78.25

Solving for variable 'x'.

Reorder the terms:
9.5 + -78.25 + 6.3x + x2 = 78.25 + -78.25

Combine like terms: 9.5 + -78.25 = -68.75
-68.75 + 6.3x + x2 = 78.25 + -78.25

Combine like terms: 78.25 + -78.25 = 0.00
-68.75 + 6.3x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '68.75' to each side of the equation.
-68.75 + 6.3x + 68.75 + x2 = 0.00 + 68.75

Reorder the terms:
-68.75 + 68.75 + 6.3x + x2 = 0.00 + 68.75

Combine like terms: -68.75 + 68.75 = 0.00
0.00 + 6.3x + x2 = 0.00 + 68.75
6.3x + x2 = 0.00 + 68.75

Combine like terms: 0.00 + 68.75 = 68.75
6.3x + x2 = 68.75

The x term is 6.3x.  Take half its coefficient (3.15).
Square it (9.9225) and add it to both sides.

Add '9.9225' to each side of the equation.
6.3x + 9.9225 + x2 = 68.75 + 9.9225

Reorder the terms:
9.9225 + 6.3x + x2 = 68.75 + 9.9225

Combine like terms: 68.75 + 9.9225 = 78.6725
9.9225 + 6.3x + x2 = 78.6725

Factor a perfect square on the left side:
(x + 3.15)(x + 3.15) = 78.6725

Calculate the square root of the right side: 8.869751969

Break this problem into two subproblems by setting 
(x + 3.15) equal to 8.869751969 and -8.869751969.


Subproblem 1
x + 3.15 = 8.869751969

Simplifying
x + 3.15 = 8.869751969

Reorder the terms:
3.15 + x = 8.869751969

Solving
3.15 + x = 8.869751969

Solving for variable 'x'.

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

Add '-3.15' to each side of the equation.
3.15 + -3.15 + x = 8.869751969 + -3.15

Combine like terms: 3.15 + -3.15 = 0.00
0.00 + x = 8.869751969 + -3.15
x = 8.869751969 + -3.15

Combine like terms: 8.869751969 + -3.15 = 5.719751969
x = 5.719751969

Simplifying
x = 5.719751969


Subproblem 2
x + 3.15 = -8.869751969

Simplifying
x + 3.15 = -8.869751969

Reorder the terms:
3.15 + x = -8.869751969

Solving
3.15 + x = -8.869751969

Solving for variable 'x'.

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

Add '-3.15' to each side of the equation.
3.15 + -3.15 + x = -8.869751969 + -3.15

Combine like terms: 3.15 + -3.15 = 0.00
0.00 + x = -8.869751969 + -3.15
x = -8.869751969 + -3.15

Combine like terms: -8.869751969 + -3.15 = -12.019751969
x = -12.019751969

Simplifying
x = -12.019751969


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.719751969, -12.019751969}

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