9p^2=8p+13

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Solution for 9p^2=8p+13 equation:


Simplifying
9p2 = 8p + 13

Reorder the terms:
9p2 = 13 + 8p

Solving
9p2 = 13 + 8p

Solving for variable 'p'.

Reorder the terms:
-13 + -8p + 9p2 = 13 + 8p + -13 + -8p

Reorder the terms:
-13 + -8p + 9p2 = 13 + -13 + 8p + -8p

Combine like terms: 13 + -13 = 0
-13 + -8p + 9p2 = 0 + 8p + -8p
-13 + -8p + 9p2 = 8p + -8p

Combine like terms: 8p + -8p = 0
-13 + -8p + 9p2 = 0

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

Divide each side by '9'.
-1.444444444 + -0.8888888889p + p2 = 0

Move the constant term to the right:

Add '1.444444444' to each side of the equation.
-1.444444444 + -0.8888888889p + 1.444444444 + p2 = 0 + 1.444444444

Reorder the terms:
-1.444444444 + 1.444444444 + -0.8888888889p + p2 = 0 + 1.444444444

Combine like terms: -1.444444444 + 1.444444444 = 0.000000000
0.000000000 + -0.8888888889p + p2 = 0 + 1.444444444
-0.8888888889p + p2 = 0 + 1.444444444

Combine like terms: 0 + 1.444444444 = 1.444444444
-0.8888888889p + p2 = 1.444444444

The p term is -0.8888888889p.  Take half its coefficient (-0.4444444445).
Square it (0.1975308642) and add it to both sides.

Add '0.1975308642' to each side of the equation.
-0.8888888889p + 0.1975308642 + p2 = 1.444444444 + 0.1975308642

Reorder the terms:
0.1975308642 + -0.8888888889p + p2 = 1.444444444 + 0.1975308642

Combine like terms: 1.444444444 + 0.1975308642 = 1.6419753082
0.1975308642 + -0.8888888889p + p2 = 1.6419753082

Factor a perfect square on the left side:
(p + -0.4444444445)(p + -0.4444444445) = 1.6419753082

Calculate the square root of the right side: 1.281395844

Break this problem into two subproblems by setting 
(p + -0.4444444445) equal to 1.281395844 and -1.281395844.

Subproblem 1

p + -0.4444444445 = 1.281395844 Simplifying p + -0.4444444445 = 1.281395844 Reorder the terms: -0.4444444445 + p = 1.281395844 Solving -0.4444444445 + p = 1.281395844 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + p = 1.281395844 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + p = 1.281395844 + 0.4444444445 p = 1.281395844 + 0.4444444445 Combine like terms: 1.281395844 + 0.4444444445 = 1.7258402885 p = 1.7258402885 Simplifying p = 1.7258402885

Subproblem 2

p + -0.4444444445 = -1.281395844 Simplifying p + -0.4444444445 = -1.281395844 Reorder the terms: -0.4444444445 + p = -1.281395844 Solving -0.4444444445 + p = -1.281395844 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + p = -1.281395844 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + p = -1.281395844 + 0.4444444445 p = -1.281395844 + 0.4444444445 Combine like terms: -1.281395844 + 0.4444444445 = -0.8369513995 p = -0.8369513995 Simplifying p = -0.8369513995

Solution

The solution to the problem is based on the solutions from the subproblems. p = {1.7258402885, -0.8369513995}

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