p^2-9p+10=0

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


Simplifying
p2 + -9p + 10 = 0

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

Solving
10 + -9p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -9p + -10 + p2 = 0 + -10

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

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

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

The p term is -9p.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9p + 20.25 + p2 = -10 + 20.25

Reorder the terms:
20.25 + -9p + p2 = -10 + 20.25

Combine like terms: -10 + 20.25 = 10.25
20.25 + -9p + p2 = 10.25

Factor a perfect square on the left side:
(p + -4.5)(p + -4.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(p + -4.5) equal to 3.201562119 and -3.201562119.

Subproblem 1

p + -4.5 = 3.201562119 Simplifying p + -4.5 = 3.201562119 Reorder the terms: -4.5 + p = 3.201562119 Solving -4.5 + p = 3.201562119 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + p = 3.201562119 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = 3.201562119 + 4.5 p = 3.201562119 + 4.5 Combine like terms: 3.201562119 + 4.5 = 7.701562119 p = 7.701562119 Simplifying p = 7.701562119

Subproblem 2

p + -4.5 = -3.201562119 Simplifying p + -4.5 = -3.201562119 Reorder the terms: -4.5 + p = -3.201562119 Solving -4.5 + p = -3.201562119 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + p = -3.201562119 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = -3.201562119 + 4.5 p = -3.201562119 + 4.5 Combine like terms: -3.201562119 + 4.5 = 1.298437881 p = 1.298437881 Simplifying p = 1.298437881

Solution

The solution to the problem is based on the solutions from the subproblems. p = {7.701562119, 1.298437881}

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