(2x+5)2x+5=25

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Solution for (2x+5)2x+5=25 equation:


Simplifying
(2x + 5) * 2x + 5 = 25

Reorder the terms:
(5 + 2x) * 2x + 5 = 25

Reorder the terms for easier multiplication:
2x(5 + 2x) + 5 = 25
(5 * 2x + 2x * 2x) + 5 = 25
(10x + 4x2) + 5 = 25

Reorder the terms:
5 + 10x + 4x2 = 25

Solving
5 + 10x + 4x2 = 25

Solving for variable 'x'.

Reorder the terms:
5 + -25 + 10x + 4x2 = 25 + -25

Combine like terms: 5 + -25 = -20
-20 + 10x + 4x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-20 + 10x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 5x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-10 + 5x + 2x2)' equal to zero and attempt to solve:

Simplifying
-10 + 5x + 2x2 = 0

Solving
-10 + 5x + 2x2 = 0

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

Divide each side by '2'.
-5 + 2.5x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 2.5x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 2.5x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2.5x + x2 = 0 + 5
2.5x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
2.5x + x2 = 5

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 5 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 5 + 1.5625

Combine like terms: 5 + 1.5625 = 6.5625
1.5625 + 2.5x + x2 = 6.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 6.5625

Calculate the square root of the right side: 2.561737691

Break this problem into two subproblems by setting 
(x + 1.25) equal to 2.561737691 and -2.561737691.


Subproblem 1
x + 1.25 = 2.561737691

Simplifying
x + 1.25 = 2.561737691

Reorder the terms:
1.25 + x = 2.561737691

Solving
1.25 + x = 2.561737691

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 2.561737691 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 2.561737691 + -1.25
x = 2.561737691 + -1.25

Combine like terms: 2.561737691 + -1.25 = 1.311737691
x = 1.311737691

Simplifying
x = 1.311737691


Subproblem 2
x + 1.25 = -2.561737691

Simplifying
x + 1.25 = -2.561737691

Reorder the terms:
1.25 + x = -2.561737691

Solving
1.25 + x = -2.561737691

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -2.561737691 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -2.561737691 + -1.25
x = -2.561737691 + -1.25

Combine like terms: -2.561737691 + -1.25 = -3.811737691
x = -3.811737691

Simplifying
x = -3.811737691


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.311737691, -3.811737691}
Solution
x = {1.311737691, -3.811737691}

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