(38-x)*(32-x)=626

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Solution for (38-x)*(32-x)=626 equation: 


Simplifying
(38 + -1x)(32 + -1x) = 626

Multiply (38 + -1x) * (32 + -1x)
(38(32 + -1x) + -1x * (32 + -1x)) = 626
((32 * 38 + -1x * 38) + -1x * (32 + -1x)) = 626
((1216 + -38x) + -1x * (32 + -1x)) = 626
(1216 + -38x + (32 * -1x + -1x * -1x)) = 626
(1216 + -38x + (-32x + 1x2)) = 626

Combine like terms: -38x + -32x = -70x
(1216 + -70x + 1x2) = 626

Solving
1216 + -70x + 1x2 = 626

Solving for variable 'x'.

Reorder the terms:
1216 + -626 + -70x + 1x2 = 626 + -626

Combine like terms: 1216 + -626 = 590
590 + -70x + 1x2 = 626 + -626

Combine like terms: 626 + -626 = 0
590 + -70x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-590' to each side of the equation.
590 + -70x + -590 + x2 = 0 + -590

Reorder the terms:
590 + -590 + -70x + x2 = 0 + -590

Combine like terms: 590 + -590 = 0
0 + -70x + x2 = 0 + -590
-70x + x2 = 0 + -590

Combine like terms: 0 + -590 = -590
-70x + x2 = -590

The x term is -70x.  Take half its coefficient (-35).
Square it (1225) and add it to both sides.

Add '1225' to each side of the equation.
-70x + 1225 + x2 = -590 + 1225

Reorder the terms:
1225 + -70x + x2 = -590 + 1225

Combine like terms: -590 + 1225 = 635
1225 + -70x + x2 = 635

Factor a perfect square on the left side:
(x + -35)(x + -35) = 635

Calculate the square root of the right side: 25.199206337

Break this problem into two subproblems by setting 
(x + -35) equal to 25.199206337 and -25.199206337.


Subproblem 1
x + -35 = 25.199206337

Simplifying
x + -35 = 25.199206337

Reorder the terms:
-35 + x = 25.199206337

Solving
-35 + x = 25.199206337

Solving for variable 'x'.

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

Add '35' to each side of the equation.
-35 + 35 + x = 25.199206337 + 35

Combine like terms: -35 + 35 = 0
0 + x = 25.199206337 + 35
x = 25.199206337 + 35

Combine like terms: 25.199206337 + 35 = 60.199206337
x = 60.199206337

Simplifying
x = 60.199206337


Subproblem 2
x + -35 = -25.199206337

Simplifying
x + -35 = -25.199206337

Reorder the terms:
-35 + x = -25.199206337

Solving
-35 + x = -25.199206337

Solving for variable 'x'.

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

Add '35' to each side of the equation.
-35 + 35 + x = -25.199206337 + 35

Combine like terms: -35 + 35 = 0
0 + x = -25.199206337 + 35
x = -25.199206337 + 35

Combine like terms: -25.199206337 + 35 = 9.800793663
x = 9.800793663

Simplifying
x = 9.800793663


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {60.199206337, 9.800793663}

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