5p^2+10p-1=0

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Solution for 5p^2+10p-1=0 equation:


Simplifying
5p2 + 10p + -1 = 0

Reorder the terms:
-1 + 10p + 5p2 = 0

Solving
-1 + 10p + 5p2 = 0

Solving for variable 'p'.

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

Divide each side by '5'.
-0.2 + 2p + p2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + 2p + 0.2 + p2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + 2p + p2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + 2p + p2 = 0 + 0.2
2p + p2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
2p + p2 = 0.2

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 = 0.2 + 1

Reorder the terms:
1 + 2p + p2 = 0.2 + 1

Combine like terms: 0.2 + 1 = 1.2
1 + 2p + p2 = 1.2

Factor a perfect square on the left side:
(p + 1)(p + 1) = 1.2

Calculate the square root of the right side: 1.095445115

Break this problem into two subproblems by setting 
(p + 1) equal to 1.095445115 and -1.095445115.

Subproblem 1

p + 1 = 1.095445115 Simplifying p + 1 = 1.095445115 Reorder the terms: 1 + p = 1.095445115 Solving 1 + p = 1.095445115 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 = 1.095445115 + -1 Combine like terms: 1 + -1 = 0 0 + p = 1.095445115 + -1 p = 1.095445115 + -1 Combine like terms: 1.095445115 + -1 = 0.095445115 p = 0.095445115 Simplifying p = 0.095445115

Subproblem 2

p + 1 = -1.095445115 Simplifying p + 1 = -1.095445115 Reorder the terms: 1 + p = -1.095445115 Solving 1 + p = -1.095445115 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 = -1.095445115 + -1 Combine like terms: 1 + -1 = 0 0 + p = -1.095445115 + -1 p = -1.095445115 + -1 Combine like terms: -1.095445115 + -1 = -2.095445115 p = -2.095445115 Simplifying p = -2.095445115

Solution

The solution to the problem is based on the solutions from the subproblems. p = {0.095445115, -2.095445115}

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