4x^2+20x+25=7

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Solution for 4x^2+20x+25=7 equation: 


Simplifying
4x2 + 20x + 25 = 7

Reorder the terms:
25 + 20x + 4x2 = 7

Solving
25 + 20x + 4x2 = 7

Solving for variable 'x'.

Reorder the terms:
25 + -7 + 20x + 4x2 = 7 + -7

Combine like terms: 25 + -7 = 18
18 + 20x + 4x2 = 7 + -7

Combine like terms: 7 + -7 = 0
18 + 20x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 10x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(9 + 10x + 2x2)' equal to zero and attempt to solve:

Simplifying
9 + 10x + 2x2 = 0

Solving
9 + 10x + 2x2 = 0

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

Divide each side by '2'.
4.5 + 5x + x2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + 5x + -4.5 + x2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + 5x + x2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + 5x + x2 = 0 + -4.5
5x + x2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
5x + x2 = -4.5

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -4.5 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -4.5 + 6.25

Combine like terms: -4.5 + 6.25 = 1.75
6.25 + 5x + x2 = 1.75

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(x + 2.5) equal to 1.322875656 and -1.322875656.


Subproblem 1
x + 2.5 = 1.322875656

Simplifying
x + 2.5 = 1.322875656

Reorder the terms:
2.5 + x = 1.322875656

Solving
2.5 + x = 1.322875656

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 1.322875656 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 1.322875656 + -2.5
x = 1.322875656 + -2.5

Combine like terms: 1.322875656 + -2.5 = -1.177124344
x = -1.177124344

Simplifying
x = -1.177124344


Subproblem 2
x + 2.5 = -1.322875656

Simplifying
x + 2.5 = -1.322875656

Reorder the terms:
2.5 + x = -1.322875656

Solving
2.5 + x = -1.322875656

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -1.322875656 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -1.322875656 + -2.5
x = -1.322875656 + -2.5

Combine like terms: -1.322875656 + -2.5 = -3.822875656
x = -3.822875656

Simplifying
x = -3.822875656


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.177124344, -3.822875656}
Solution
x = {-1.177124344, -3.822875656}

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