10p^2+4p-10=0

Solution for 10p^2+4p-10=0 equation:

Simplifying
10p2 + 4p + -10 = 0

Reorder the terms:
-10 + 4p + 10p2 = 0

Solving
-10 + 4p + 10p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 2p + 5p2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + 2p + 5p2)' equal to zero and attempt to solve:

Simplifying
-5 + 2p + 5p2 = 0

Solving
-5 + 2p + 5p2 = 0

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

Divide each side by '5'.
-1 + 0.4p + p2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.4p + 1 + p2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.4p + p2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.4p + p2 = 0 + 1
0.4p + p2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.4p + p2 = 1

The p term is 0.4p.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4p + 0.04 + p2 = 1 + 0.04

Reorder the terms:
0.04 + 0.4p + p2 = 1 + 0.04

Combine like terms: 1 + 0.04 = 1.04
0.04 + 0.4p + p2 = 1.04

Factor a perfect square on the left side:
(p + 0.2)(p + 0.2) = 1.04

Calculate the square root of the right side: 1.019803903

Break this problem into two subproblems by setting 
(p + 0.2) equal to 1.019803903 and -1.019803903.

Subproblem 1
p + 0.2 = 1.019803903

Simplifying
p + 0.2 = 1.019803903

Reorder the terms:
0.2 + p = 1.019803903

Solving
0.2 + p = 1.019803903

Solving for variable 'p'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + p = 1.019803903 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + p = 1.019803903 + -0.2
p = 1.019803903 + -0.2

Combine like terms: 1.019803903 + -0.2 = 0.819803903
p = 0.819803903

Simplifying
p = 0.819803903

Subproblem 2
p + 0.2 = -1.019803903

Simplifying
p + 0.2 = -1.019803903

Reorder the terms:
0.2 + p = -1.019803903

Solving
0.2 + p = -1.019803903

Solving for variable 'p'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + p = -1.019803903 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + p = -1.019803903 + -0.2
p = -1.019803903 + -0.2

Combine like terms: -1.019803903 + -0.2 = -1.219803903
p = -1.219803903

Simplifying
p = -1.219803903

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.819803903, -1.219803903}
Solution
p = {0.819803903, -1.219803903}