12p^2+1=-9p

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Solution for 12p^2+1=-9p equation:


Simplifying
12p2 + 1 = -9p

Reorder the terms:
1 + 12p2 = -9p

Solving
1 + 12p2 = -9p

Solving for variable 'p'.

Reorder the terms:
1 + 9p + 12p2 = -9p + 9p

Combine like terms: -9p + 9p = 0
1 + 9p + 12p2 = 0

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

Divide each side by '12'.
0.08333333333 + 0.75p + p2 = 0

Move the constant term to the right:

Add '-0.08333333333' to each side of the equation.
0.08333333333 + 0.75p + -0.08333333333 + p2 = 0 + -0.08333333333

Reorder the terms:
0.08333333333 + -0.08333333333 + 0.75p + p2 = 0 + -0.08333333333

Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000
0.00000000000 + 0.75p + p2 = 0 + -0.08333333333
0.75p + p2 = 0 + -0.08333333333

Combine like terms: 0 + -0.08333333333 = -0.08333333333
0.75p + p2 = -0.08333333333

The p term is 0.75p.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75p + 0.140625 + p2 = -0.08333333333 + 0.140625

Reorder the terms:
0.140625 + 0.75p + p2 = -0.08333333333 + 0.140625

Combine like terms: -0.08333333333 + 0.140625 = 0.05729166667
0.140625 + 0.75p + p2 = 0.05729166667

Factor a perfect square on the left side:
(p + 0.375)(p + 0.375) = 0.05729166667

Calculate the square root of the right side: 0.239356777

Break this problem into two subproblems by setting 
(p + 0.375) equal to 0.239356777 and -0.239356777.

Subproblem 1

p + 0.375 = 0.239356777 Simplifying p + 0.375 = 0.239356777 Reorder the terms: 0.375 + p = 0.239356777 Solving 0.375 + p = 0.239356777 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + p = 0.239356777 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + p = 0.239356777 + -0.375 p = 0.239356777 + -0.375 Combine like terms: 0.239356777 + -0.375 = -0.135643223 p = -0.135643223 Simplifying p = -0.135643223

Subproblem 2

p + 0.375 = -0.239356777 Simplifying p + 0.375 = -0.239356777 Reorder the terms: 0.375 + p = -0.239356777 Solving 0.375 + p = -0.239356777 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + p = -0.239356777 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + p = -0.239356777 + -0.375 p = -0.239356777 + -0.375 Combine like terms: -0.239356777 + -0.375 = -0.614356777 p = -0.614356777 Simplifying p = -0.614356777

Solution

The solution to the problem is based on the solutions from the subproblems. p = {-0.135643223, -0.614356777}

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