907.27=[(30+x)(35+x)]-(30*35)

Solution for 907.27=[(30+x)(35+x)]-(30*35) equation:

Simplifying
907.27 = [(30 + x)(35 + x)] + -1(30 * 35)

Multiply (30 + x) * (35 + x)
907.27 = [(30(35 + x) + x(35 + x))] + -1(30 * 35)
907.27 = [((35 * 30 + x * 30) + x(35 + x))] + -1(30 * 35)
907.27 = [((1050 + 30x) + x(35 + x))] + -1(30 * 35)
907.27 = [(1050 + 30x + (35 * x + x * x))] + -1(30 * 35)
907.27 = [(1050 + 30x + (35x + x2))] + -1(30 * 35)

Combine like terms: 30x + 35x = 65x
907.27 = [(1050 + 65x + x2)] + -1(30 * 35)
907.27 = [1050 + 65x + x2] + -1(30 * 35)

Remove brackets around [1050 + 65x + x2]
907.27 = 1050 + 65x + x2 + -1(30 * 35)

Multiply 30 * 35
907.27 = 1050 + 65x + x2 + -1(1050)

Multiply -1 * 1050
907.27 = 1050 + 65x + x2 + -1050

Reorder the terms:
907.27 = 1050 + -1050 + 65x + x2

Combine like terms: 1050 + -1050 = 0
907.27 = 0 + 65x + x2
907.27 = 65x + x2

Solving
907.27 = 65x + x2

Solving for variable 'x'.

Reorder the terms:
907.27 + -65x + -1x2 = 65x + -65x + x2 + -1x2

Combine like terms: 65x + -65x = 0
907.27 + -65x + -1x2 = 0 + x2 + -1x2
907.27 + -65x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
907.27 + -65x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-907.27 + 65x + x2 = 0

Move the constant term to the right:

Add '907.27' to each side of the equation.
-907.27 + 65x + 907.27 + x2 = 0 + 907.27

Reorder the terms:
-907.27 + 907.27 + 65x + x2 = 0 + 907.27

Combine like terms: -907.27 + 907.27 = 0.00
0.00 + 65x + x2 = 0 + 907.27
65x + x2 = 0 + 907.27

Combine like terms: 0 + 907.27 = 907.27
65x + x2 = 907.27

The x term is 65x.  Take half its coefficient (32.5).
Square it (1056.25) and add it to both sides.

Add '1056.25' to each side of the equation.
65x + 1056.25 + x2 = 907.27 + 1056.25

Reorder the terms:
1056.25 + 65x + x2 = 907.27 + 1056.25

Combine like terms: 907.27 + 1056.25 = 1963.52
1056.25 + 65x + x2 = 1963.52

Factor a perfect square on the left side:
(x + 32.5)(x + 32.5) = 1963.52

Calculate the square root of the right side: 44.311623757

Break this problem into two subproblems by setting 
(x + 32.5) equal to 44.311623757 and -44.311623757.

Subproblem 1
x + 32.5 = 44.311623757

Simplifying
x + 32.5 = 44.311623757

Reorder the terms:
32.5 + x = 44.311623757

Solving
32.5 + x = 44.311623757

Solving for variable 'x'.

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

Add '-32.5' to each side of the equation.
32.5 + -32.5 + x = 44.311623757 + -32.5

Combine like terms: 32.5 + -32.5 = 0.0
0.0 + x = 44.311623757 + -32.5
x = 44.311623757 + -32.5

Combine like terms: 44.311623757 + -32.5 = 11.811623757
x = 11.811623757

Simplifying
x = 11.811623757

Subproblem 2
x + 32.5 = -44.311623757

Simplifying
x + 32.5 = -44.311623757

Reorder the terms:
32.5 + x = -44.311623757

Solving
32.5 + x = -44.311623757

Solving for variable 'x'.

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

Add '-32.5' to each side of the equation.
32.5 + -32.5 + x = -44.311623757 + -32.5

Combine like terms: 32.5 + -32.5 = 0.0
0.0 + x = -44.311623757 + -32.5
x = -44.311623757 + -32.5

Combine like terms: -44.311623757 + -32.5 = -76.811623757
x = -76.811623757

Simplifying
x = -76.811623757

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.811623757, -76.811623757}