10p^2+7p=1

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Solution for 10p^2+7p=1 equation:


Simplifying
10p2 + 7p = 1

Reorder the terms:
7p + 10p2 = 1

Solving
7p + 10p2 = 1

Solving for variable 'p'.

Reorder the terms:
-1 + 7p + 10p2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 7p + 10p2 = 0

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

Divide each side by '10'.
-0.1 + 0.7p + p2 = 0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + 0.7p + 0.1 + p2 = 0 + 0.1

Reorder the terms:
-0.1 + 0.1 + 0.7p + p2 = 0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + 0.7p + p2 = 0 + 0.1
0.7p + p2 = 0 + 0.1

Combine like terms: 0 + 0.1 = 0.1
0.7p + p2 = 0.1

The p term is 0.7p.  Take half its coefficient (0.35).
Square it (0.1225) and add it to both sides.

Add '0.1225' to each side of the equation.
0.7p + 0.1225 + p2 = 0.1 + 0.1225

Reorder the terms:
0.1225 + 0.7p + p2 = 0.1 + 0.1225

Combine like terms: 0.1 + 0.1225 = 0.2225
0.1225 + 0.7p + p2 = 0.2225

Factor a perfect square on the left side:
(p + 0.35)(p + 0.35) = 0.2225

Calculate the square root of the right side: 0.471699057

Break this problem into two subproblems by setting 
(p + 0.35) equal to 0.471699057 and -0.471699057.

Subproblem 1

p + 0.35 = 0.471699057 Simplifying p + 0.35 = 0.471699057 Reorder the terms: 0.35 + p = 0.471699057 Solving 0.35 + p = 0.471699057 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + p = 0.471699057 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + p = 0.471699057 + -0.35 p = 0.471699057 + -0.35 Combine like terms: 0.471699057 + -0.35 = 0.121699057 p = 0.121699057 Simplifying p = 0.121699057

Subproblem 2

p + 0.35 = -0.471699057 Simplifying p + 0.35 = -0.471699057 Reorder the terms: 0.35 + p = -0.471699057 Solving 0.35 + p = -0.471699057 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + p = -0.471699057 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + p = -0.471699057 + -0.35 p = -0.471699057 + -0.35 Combine like terms: -0.471699057 + -0.35 = -0.821699057 p = -0.821699057 Simplifying p = -0.821699057

Solution

The solution to the problem is based on the solutions from the subproblems. p = {0.121699057, -0.821699057}

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