p^2-17p+21=0

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Solution for p^2-17p+21=0 equation:


Simplifying
p2 + -17p + 21 = 0

Reorder the terms:
21 + -17p + p2 = 0

Solving
21 + -17p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + -17p + -21 + p2 = 0 + -21

Reorder the terms:
21 + -21 + -17p + p2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -17p + p2 = 0 + -21
-17p + p2 = 0 + -21

Combine like terms: 0 + -21 = -21
-17p + p2 = -21

The p term is -17p.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17p + 72.25 + p2 = -21 + 72.25

Reorder the terms:
72.25 + -17p + p2 = -21 + 72.25

Combine like terms: -21 + 72.25 = 51.25
72.25 + -17p + p2 = 51.25

Factor a perfect square on the left side:
(p + -8.5)(p + -8.5) = 51.25

Calculate the square root of the right side: 7.158910532

Break this problem into two subproblems by setting 
(p + -8.5) equal to 7.158910532 and -7.158910532.

Subproblem 1

p + -8.5 = 7.158910532 Simplifying p + -8.5 = 7.158910532 Reorder the terms: -8.5 + p = 7.158910532 Solving -8.5 + p = 7.158910532 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + p = 7.158910532 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + p = 7.158910532 + 8.5 p = 7.158910532 + 8.5 Combine like terms: 7.158910532 + 8.5 = 15.658910532 p = 15.658910532 Simplifying p = 15.658910532

Subproblem 2

p + -8.5 = -7.158910532 Simplifying p + -8.5 = -7.158910532 Reorder the terms: -8.5 + p = -7.158910532 Solving -8.5 + p = -7.158910532 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + p = -7.158910532 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + p = -7.158910532 + 8.5 p = -7.158910532 + 8.5 Combine like terms: -7.158910532 + 8.5 = 1.341089468 p = 1.341089468 Simplifying p = 1.341089468

Solution

The solution to the problem is based on the solutions from the subproblems. p = {15.658910532, 1.341089468}

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