2p^2+4p-1=7p-7p+1

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

Simplifying
2p2 + 4p + -1 = 7p + -7p + 1

Reorder the terms:
-1 + 4p + 2p2 = 7p + -7p + 1

Reorder the terms:
-1 + 4p + 2p2 = 1 + 7p + -7p

Combine like terms: 7p + -7p = 0
-1 + 4p + 2p2 = 1 + 0
-1 + 4p + 2p2 = 1

Solving
-1 + 4p + 2p2 = 1

Solving for variable 'p'.

Reorder the terms:
-1 + -1 + 4p + 2p2 = 1 + -1

Combine like terms: -1 + -1 = -2
-2 + 4p + 2p2 = 1 + -1

Combine like terms: 1 + -1 = 0
-2 + 4p + 2p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 2p + p2) = 0

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

Simplifying
-1 + 2p + p2 = 0

Solving
-1 + 2p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 2p + 1 + p2 = 0 + 1

Reorder the terms:
-1 + 1 + 2p + p2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2p + p2 = 0 + 1
2p + p2 = 0 + 1

Combine like terms: 0 + 1 = 1
2p + p2 = 1

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

Add '1' to each side of the equation.
2p + 1 + p2 = 1 + 1

Reorder the terms:
1 + 2p + p2 = 1 + 1

Combine like terms: 1 + 1 = 2
1 + 2p + p2 = 2

Factor a perfect square on the left side:
(p + 1)(p + 1) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(p + 1) equal to 1.414213562 and -1.414213562.

Subproblem 1
p + 1 = 1.414213562

Simplifying
p + 1 = 1.414213562

Reorder the terms:
1 + p = 1.414213562

Solving
1 + p = 1.414213562

Solving for variable 'p'.

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

Add '-1' to each side of the equation.
1 + -1 + p = 1.414213562 + -1

Combine like terms: 1 + -1 = 0
0 + p = 1.414213562 + -1
p = 1.414213562 + -1

Combine like terms: 1.414213562 + -1 = 0.414213562
p = 0.414213562

Simplifying
p = 0.414213562

Subproblem 2
p + 1 = -1.414213562

Simplifying
p + 1 = -1.414213562

Reorder the terms:
1 + p = -1.414213562

Solving
1 + p = -1.414213562

Solving for variable 'p'.

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

Add '-1' to each side of the equation.
1 + -1 + p = -1.414213562 + -1

Combine like terms: 1 + -1 = 0
0 + p = -1.414213562 + -1
p = -1.414213562 + -1

Combine like terms: -1.414213562 + -1 = -2.414213562
p = -2.414213562

Simplifying
p = -2.414213562

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.414213562, -2.414213562}
Solution
p = {0.414213562, -2.414213562}