9p^2+7p-56=0

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Solution for 9p^2+7p-56=0 equation:


Simplifying
9p2 + 7p + -56 = 0

Reorder the terms:
-56 + 7p + 9p2 = 0

Solving
-56 + 7p + 9p2 = 0

Solving for variable 'p'.

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

Divide each side by '9'.
-6.222222222 + 0.7777777778p + p2 = 0

Move the constant term to the right:

Add '6.222222222' to each side of the equation.
-6.222222222 + 0.7777777778p + 6.222222222 + p2 = 0 + 6.222222222

Reorder the terms:
-6.222222222 + 6.222222222 + 0.7777777778p + p2 = 0 + 6.222222222

Combine like terms: -6.222222222 + 6.222222222 = 0.000000000
0.000000000 + 0.7777777778p + p2 = 0 + 6.222222222
0.7777777778p + p2 = 0 + 6.222222222

Combine like terms: 0 + 6.222222222 = 6.222222222
0.7777777778p + p2 = 6.222222222

The p term is 0.7777777778p.  Take half its coefficient (0.3888888889).
Square it (0.1512345679) and add it to both sides.

Add '0.1512345679' to each side of the equation.
0.7777777778p + 0.1512345679 + p2 = 6.222222222 + 0.1512345679

Reorder the terms:
0.1512345679 + 0.7777777778p + p2 = 6.222222222 + 0.1512345679

Combine like terms: 6.222222222 + 0.1512345679 = 6.3734567899
0.1512345679 + 0.7777777778p + p2 = 6.3734567899

Factor a perfect square on the left side:
(p + 0.3888888889)(p + 0.3888888889) = 6.3734567899

Calculate the square root of the right side: 2.524570615

Break this problem into two subproblems by setting 
(p + 0.3888888889) equal to 2.524570615 and -2.524570615.

Subproblem 1

p + 0.3888888889 = 2.524570615 Simplifying p + 0.3888888889 = 2.524570615 Reorder the terms: 0.3888888889 + p = 2.524570615 Solving 0.3888888889 + p = 2.524570615 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.3888888889' to each side of the equation. 0.3888888889 + -0.3888888889 + p = 2.524570615 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + p = 2.524570615 + -0.3888888889 p = 2.524570615 + -0.3888888889 Combine like terms: 2.524570615 + -0.3888888889 = 2.1356817261 p = 2.1356817261 Simplifying p = 2.1356817261

Subproblem 2

p + 0.3888888889 = -2.524570615 Simplifying p + 0.3888888889 = -2.524570615 Reorder the terms: 0.3888888889 + p = -2.524570615 Solving 0.3888888889 + p = -2.524570615 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.3888888889' to each side of the equation. 0.3888888889 + -0.3888888889 + p = -2.524570615 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + p = -2.524570615 + -0.3888888889 p = -2.524570615 + -0.3888888889 Combine like terms: -2.524570615 + -0.3888888889 = -2.9134595039 p = -2.9134595039 Simplifying p = -2.9134595039

Solution

The solution to the problem is based on the solutions from the subproblems. p = {2.1356817261, -2.9134595039}

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