(2x+10)(2x+15)=250

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Solution for (2x+10)(2x+15)=250 equation: 


Simplifying
(2x + 10)(2x + 15) = 250

Reorder the terms:
(10 + 2x)(2x + 15) = 250

Reorder the terms:
(10 + 2x)(15 + 2x) = 250

Multiply (10 + 2x) * (15 + 2x)
(10(15 + 2x) + 2x * (15 + 2x)) = 250
((15 * 10 + 2x * 10) + 2x * (15 + 2x)) = 250
((150 + 20x) + 2x * (15 + 2x)) = 250
(150 + 20x + (15 * 2x + 2x * 2x)) = 250
(150 + 20x + (30x + 4x2)) = 250

Combine like terms: 20x + 30x = 50x
(150 + 50x + 4x2) = 250

Solving
150 + 50x + 4x2 = 250

Solving for variable 'x'.

Reorder the terms:
150 + -250 + 50x + 4x2 = 250 + -250

Combine like terms: 150 + -250 = -100
-100 + 50x + 4x2 = 250 + -250

Combine like terms: 250 + -250 = 0
-100 + 50x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + 25x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-50 + 25x + 2x2)' equal to zero and attempt to solve:

Simplifying
-50 + 25x + 2x2 = 0

Solving
-50 + 25x + 2x2 = 0

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

Divide each side by '2'.
-25 + 12.5x + x2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 12.5x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + 12.5x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 12.5x + x2 = 0 + 25
12.5x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
12.5x + x2 = 25

The x term is 12.5x.  Take half its coefficient (6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
12.5x + 39.0625 + x2 = 25 + 39.0625

Reorder the terms:
39.0625 + 12.5x + x2 = 25 + 39.0625

Combine like terms: 25 + 39.0625 = 64.0625
39.0625 + 12.5x + x2 = 64.0625

Factor a perfect square on the left side:
(x + 6.25)(x + 6.25) = 64.0625

Calculate the square root of the right side: 8.003905297

Break this problem into two subproblems by setting 
(x + 6.25) equal to 8.003905297 and -8.003905297.


Subproblem 1
x + 6.25 = 8.003905297

Simplifying
x + 6.25 = 8.003905297

Reorder the terms:
6.25 + x = 8.003905297

Solving
6.25 + x = 8.003905297

Solving for variable 'x'.

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

Add '-6.25' to each side of the equation.
6.25 + -6.25 + x = 8.003905297 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + x = 8.003905297 + -6.25
x = 8.003905297 + -6.25

Combine like terms: 8.003905297 + -6.25 = 1.753905297
x = 1.753905297

Simplifying
x = 1.753905297


Subproblem 2
x + 6.25 = -8.003905297

Simplifying
x + 6.25 = -8.003905297

Reorder the terms:
6.25 + x = -8.003905297

Solving
6.25 + x = -8.003905297

Solving for variable 'x'.

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

Add '-6.25' to each side of the equation.
6.25 + -6.25 + x = -8.003905297 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + x = -8.003905297 + -6.25
x = -8.003905297 + -6.25

Combine like terms: -8.003905297 + -6.25 = -14.253905297
x = -14.253905297

Simplifying
x = -14.253905297


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.753905297, -14.253905297}
Solution
x = {1.753905297, -14.253905297}

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