9p^2+18p=10

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Solution for 9p^2+18p=10 equation:


Simplifying
9p2 + 18p = 10

Reorder the terms:
18p + 9p2 = 10

Solving
18p + 9p2 = 10

Solving for variable 'p'.

Reorder the terms:
-10 + 18p + 9p2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 18p + 9p2 = 0

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

Divide each side by '9'.
-1.111111111 + 2p + p2 = 0

Move the constant term to the right:

Add '1.111111111' to each side of the equation.
-1.111111111 + 2p + 1.111111111 + p2 = 0 + 1.111111111

Reorder the terms:
-1.111111111 + 1.111111111 + 2p + p2 = 0 + 1.111111111

Combine like terms: -1.111111111 + 1.111111111 = 0.000000000
0.000000000 + 2p + p2 = 0 + 1.111111111
2p + p2 = 0 + 1.111111111

Combine like terms: 0 + 1.111111111 = 1.111111111
2p + p2 = 1.111111111

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 = 1.111111111 + 1

Reorder the terms:
1 + 2p + p2 = 1.111111111 + 1

Combine like terms: 1.111111111 + 1 = 2.111111111
1 + 2p + p2 = 2.111111111

Factor a perfect square on the left side:
(p + 1)(p + 1) = 2.111111111

Calculate the square root of the right side: 1.452966314

Break this problem into two subproblems by setting 
(p + 1) equal to 1.452966314 and -1.452966314.

Subproblem 1

p + 1 = 1.452966314 Simplifying p + 1 = 1.452966314 Reorder the terms: 1 + p = 1.452966314 Solving 1 + p = 1.452966314 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 = 1.452966314 + -1 Combine like terms: 1 + -1 = 0 0 + p = 1.452966314 + -1 p = 1.452966314 + -1 Combine like terms: 1.452966314 + -1 = 0.452966314 p = 0.452966314 Simplifying p = 0.452966314

Subproblem 2

p + 1 = -1.452966314 Simplifying p + 1 = -1.452966314 Reorder the terms: 1 + p = -1.452966314 Solving 1 + p = -1.452966314 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 = -1.452966314 + -1 Combine like terms: 1 + -1 = 0 0 + p = -1.452966314 + -1 p = -1.452966314 + -1 Combine like terms: -1.452966314 + -1 = -2.452966314 p = -2.452966314 Simplifying p = -2.452966314

Solution

The solution to the problem is based on the solutions from the subproblems. p = {0.452966314, -2.452966314}

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