(40+2x)(60+2x)=248

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Solution for (40+2x)(60+2x)=248 equation: 


Simplifying
(40 + 2x)(60 + 2x) = 248

Multiply (40 + 2x) * (60 + 2x)
(40(60 + 2x) + 2x * (60 + 2x)) = 248
((60 * 40 + 2x * 40) + 2x * (60 + 2x)) = 248
((2400 + 80x) + 2x * (60 + 2x)) = 248
(2400 + 80x + (60 * 2x + 2x * 2x)) = 248
(2400 + 80x + (120x + 4x2)) = 248

Combine like terms: 80x + 120x = 200x
(2400 + 200x + 4x2) = 248

Solving
2400 + 200x + 4x2 = 248

Solving for variable 'x'.

Reorder the terms:
2400 + -248 + 200x + 4x2 = 248 + -248

Combine like terms: 2400 + -248 = 2152
2152 + 200x + 4x2 = 248 + -248

Combine like terms: 248 + -248 = 0
2152 + 200x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(538 + 50x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(538 + 50x + x2)' equal to zero and attempt to solve:

Simplifying
538 + 50x + x2 = 0

Solving
538 + 50x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-538' to each side of the equation.
538 + 50x + -538 + x2 = 0 + -538

Reorder the terms:
538 + -538 + 50x + x2 = 0 + -538

Combine like terms: 538 + -538 = 0
0 + 50x + x2 = 0 + -538
50x + x2 = 0 + -538

Combine like terms: 0 + -538 = -538
50x + x2 = -538

The x term is 50x.  Take half its coefficient (25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
50x + 625 + x2 = -538 + 625

Reorder the terms:
625 + 50x + x2 = -538 + 625

Combine like terms: -538 + 625 = 87
625 + 50x + x2 = 87

Factor a perfect square on the left side:
(x + 25)(x + 25) = 87

Calculate the square root of the right side: 9.327379053

Break this problem into two subproblems by setting 
(x + 25) equal to 9.327379053 and -9.327379053.


Subproblem 1
x + 25 = 9.327379053

Simplifying
x + 25 = 9.327379053

Reorder the terms:
25 + x = 9.327379053

Solving
25 + x = 9.327379053

Solving for variable 'x'.

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

Add '-25' to each side of the equation.
25 + -25 + x = 9.327379053 + -25

Combine like terms: 25 + -25 = 0
0 + x = 9.327379053 + -25
x = 9.327379053 + -25

Combine like terms: 9.327379053 + -25 = -15.672620947
x = -15.672620947

Simplifying
x = -15.672620947


Subproblem 2
x + 25 = -9.327379053

Simplifying
x + 25 = -9.327379053

Reorder the terms:
25 + x = -9.327379053

Solving
25 + x = -9.327379053

Solving for variable 'x'.

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

Add '-25' to each side of the equation.
25 + -25 + x = -9.327379053 + -25

Combine like terms: 25 + -25 = 0
0 + x = -9.327379053 + -25
x = -9.327379053 + -25

Combine like terms: -9.327379053 + -25 = -34.327379053
x = -34.327379053

Simplifying
x = -34.327379053


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-15.672620947, -34.327379053}
Solution
x = {-15.672620947, -34.327379053}

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