2x^2+4x+1=25

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Solution for 2x^2+4x+1=25 equation: 


Simplifying
2x2 + 4x + 1 = 25

Reorder the terms:
1 + 4x + 2x2 = 25

Solving
1 + 4x + 2x2 = 25

Solving for variable 'x'.

Reorder the terms:
1 + -25 + 4x + 2x2 = 25 + -25

Combine like terms: 1 + -25 = -24
-24 + 4x + 2x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-24 + 4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 2x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-12 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-12 + 2x + x2 = 0

Solving
-12 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 2x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 2x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 2x + x2 = 0 + 12
2x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
2x + x2 = 12

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 12 + 1

Reorder the terms:
1 + 2x + x2 = 12 + 1

Combine like terms: 12 + 1 = 13
1 + 2x + x2 = 13

Factor a perfect square on the left side:
(x + 1)(x + 1) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + 1) equal to 3.605551275 and -3.605551275.


Subproblem 1
x + 1 = 3.605551275

Simplifying
x + 1 = 3.605551275

Reorder the terms:
1 + x = 3.605551275

Solving
1 + x = 3.605551275

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 3.605551275 + -1

Combine like terms: 1 + -1 = 0
0 + x = 3.605551275 + -1
x = 3.605551275 + -1

Combine like terms: 3.605551275 + -1 = 2.605551275
x = 2.605551275

Simplifying
x = 2.605551275


Subproblem 2
x + 1 = -3.605551275

Simplifying
x + 1 = -3.605551275

Reorder the terms:
1 + x = -3.605551275

Solving
1 + x = -3.605551275

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -3.605551275 + -1

Combine like terms: 1 + -1 = 0
0 + x = -3.605551275 + -1
x = -3.605551275 + -1

Combine like terms: -3.605551275 + -1 = -4.605551275
x = -4.605551275

Simplifying
x = -4.605551275


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.605551275, -4.605551275}
Solution
x = {2.605551275, -4.605551275}

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