4p^2+4p+1=7

Solution for 4p^2+4p+1=7 equation:

Simplifying
4p2 + 4p + 1 = 7

Reorder the terms:
1 + 4p + 4p2 = 7

Solving
1 + 4p + 4p2 = 7

Solving for variable 'p'.

Reorder the terms:
1 + -7 + 4p + 4p2 = 7 + -7

Combine like terms: 1 + -7 = -6
-6 + 4p + 4p2 = 7 + -7

Combine like terms: 7 + -7 = 0
-6 + 4p + 4p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 2p + 2p2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 2p + 2p2)' equal to zero and attempt to solve:

Simplifying
-3 + 2p + 2p2 = 0

Solving
-3 + 2p + 2p2 = 0

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

Divide each side by '2'.
-1.5 + p + p2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + p + 1.5 + p2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + p + p2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + p + p2 = 0 + 1.5
p + p2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
p + p2 = 1.5

The p term is p.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + p2 = 1.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + p2 = 1.5 + 0.25

Combine like terms: 1.5 + 0.25 = 1.75
1.25 + p2 = 1.75

Factor a perfect square on the left side:
(p + 0.5)(p + 0.5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(p + 0.5) equal to 1.322875656 and -1.322875656.

Subproblem 1
p + 0.5 = 1.322875656

Simplifying
p + 0.5 = 1.322875656

Reorder the terms:
0.5 + p = 1.322875656

Solving
0.5 + p = 1.322875656

Solving for variable 'p'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + p = 1.322875656 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + p = 1.322875656 + -0.5
p = 1.322875656 + -0.5

Combine like terms: 1.322875656 + -0.5 = 0.822875656
p = 0.822875656

Simplifying
p = 0.822875656

Subproblem 2
p + 0.5 = -1.322875656

Simplifying
p + 0.5 = -1.322875656

Reorder the terms:
0.5 + p = -1.322875656

Solving
0.5 + p = -1.322875656

Solving for variable 'p'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + p = -1.322875656 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + p = -1.322875656 + -0.5
p = -1.322875656 + -0.5

Combine like terms: -1.322875656 + -0.5 = -1.822875656
p = -1.822875656

Simplifying
p = -1.822875656

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.822875656, -1.822875656}
Solution
p = {0.822875656, -1.822875656}