(35+x)(x+10)=1350

Solution for (35+x)(x+10)=1350 equation:

Simplifying
(35 + x)(x + 10) = 1350

Reorder the terms:
(35 + x)(10 + x) = 1350

Multiply (35 + x) * (10 + x)
(35(10 + x) + x(10 + x)) = 1350
((10 * 35 + x * 35) + x(10 + x)) = 1350
((350 + 35x) + x(10 + x)) = 1350
(350 + 35x + (10 * x + x * x)) = 1350
(350 + 35x + (10x + x2)) = 1350

Combine like terms: 35x + 10x = 45x
(350 + 45x + x2) = 1350

Solving
350 + 45x + x2 = 1350

Solving for variable 'x'.

Reorder the terms:
350 + -1350 + 45x + x2 = 1350 + -1350

Combine like terms: 350 + -1350 = -1000
-1000 + 45x + x2 = 1350 + -1350

Combine like terms: 1350 + -1350 = 0
-1000 + 45x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1000' to each side of the equation.
-1000 + 45x + 1000 + x2 = 0 + 1000

Reorder the terms:
-1000 + 1000 + 45x + x2 = 0 + 1000

Combine like terms: -1000 + 1000 = 0
0 + 45x + x2 = 0 + 1000
45x + x2 = 0 + 1000

Combine like terms: 0 + 1000 = 1000
45x + x2 = 1000

The x term is 45x.  Take half its coefficient (22.5).
Square it (506.25) and add it to both sides.

Add '506.25' to each side of the equation.
45x + 506.25 + x2 = 1000 + 506.25

Reorder the terms:
506.25 + 45x + x2 = 1000 + 506.25

Combine like terms: 1000 + 506.25 = 1506.25
506.25 + 45x + x2 = 1506.25

Factor a perfect square on the left side:
(x + 22.5)(x + 22.5) = 1506.25

Calculate the square root of the right side: 38.810436741

Break this problem into two subproblems by setting 
(x + 22.5) equal to 38.810436741 and -38.810436741.

Subproblem 1
x + 22.5 = 38.810436741

Simplifying
x + 22.5 = 38.810436741

Reorder the terms:
22.5 + x = 38.810436741

Solving
22.5 + x = 38.810436741

Solving for variable 'x'.

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

Add '-22.5' to each side of the equation.
22.5 + -22.5 + x = 38.810436741 + -22.5

Combine like terms: 22.5 + -22.5 = 0.0
0.0 + x = 38.810436741 + -22.5
x = 38.810436741 + -22.5

Combine like terms: 38.810436741 + -22.5 = 16.310436741
x = 16.310436741

Simplifying
x = 16.310436741

Subproblem 2
x + 22.5 = -38.810436741

Simplifying
x + 22.5 = -38.810436741

Reorder the terms:
22.5 + x = -38.810436741

Solving
22.5 + x = -38.810436741

Solving for variable 'x'.

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

Add '-22.5' to each side of the equation.
22.5 + -22.5 + x = -38.810436741 + -22.5

Combine like terms: 22.5 + -22.5 = 0.0
0.0 + x = -38.810436741 + -22.5
x = -38.810436741 + -22.5

Combine like terms: -38.810436741 + -22.5 = -61.310436741
x = -61.310436741

Simplifying
x = -61.310436741

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.310436741, -61.310436741}