9p^2-24p+10=0

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Solution for 9p^2-24p+10=0 equation: 


Simplifying
9p2 + -24p + 10 = 0

Reorder the terms:
10 + -24p + 9p2 = 0

Solving
10 + -24p + 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'.
1.111111111 + -2.666666667p + p2 = 0

Move the constant term to the right:

Add '-1.111111111' to each side of the equation.
1.111111111 + -2.666666667p + -1.111111111 + p2 = 0 + -1.111111111

Reorder the terms:
1.111111111 + -1.111111111 + -2.666666667p + p2 = 0 + -1.111111111

Combine like terms: 1.111111111 + -1.111111111 = 0.000000000
0.000000000 + -2.666666667p + p2 = 0 + -1.111111111
-2.666666667p + p2 = 0 + -1.111111111

Combine like terms: 0 + -1.111111111 = -1.111111111
-2.666666667p + p2 = -1.111111111

The p term is -2.666666667p.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667p + 1.777777780 + p2 = -1.111111111 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667p + p2 = -1.111111111 + 1.777777780

Combine like terms: -1.111111111 + 1.777777780 = 0.666666669
1.777777780 + -2.666666667p + p2 = 0.666666669

Factor a perfect square on the left side:
(p + -1.333333334)(p + -1.333333334) = 0.666666669

Calculate the square root of the right side: 0.816496582

Break this problem into two subproblems by setting 
(p + -1.333333334) equal to 0.816496582 and -0.816496582.


Subproblem 1
p + -1.333333334 = 0.816496582

Simplifying
p + -1.333333334 = 0.816496582

Reorder the terms:
-1.333333334 + p = 0.816496582

Solving
-1.333333334 + p = 0.816496582

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + p = 0.816496582 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + p = 0.816496582 + 1.333333334
p = 0.816496582 + 1.333333334

Combine like terms: 0.816496582 + 1.333333334 = 2.149829916
p = 2.149829916

Simplifying
p = 2.149829916


Subproblem 2
p + -1.333333334 = -0.816496582

Simplifying
p + -1.333333334 = -0.816496582

Reorder the terms:
-1.333333334 + p = -0.816496582

Solving
-1.333333334 + p = -0.816496582

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + p = -0.816496582 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + p = -0.816496582 + 1.333333334
p = -0.816496582 + 1.333333334

Combine like terms: -0.816496582 + 1.333333334 = 0.516836752
p = 0.516836752

Simplifying
p = 0.516836752


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.149829916, 0.516836752}

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