-11p-24+p^2=

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Solution for -11p-24+p^2= equation:


Simplifying
-11p + -24 + p2 = 0

Reorder the terms:
-24 + -11p + p2 = 0

Solving
-24 + -11p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -11p + 24 + p2 = 0 + 24

Reorder the terms:
-24 + 24 + -11p + p2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -11p + p2 = 0 + 24
-11p + p2 = 0 + 24

Combine like terms: 0 + 24 = 24
-11p + p2 = 24

The p term is -11p.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11p + 30.25 + p2 = 24 + 30.25

Reorder the terms:
30.25 + -11p + p2 = 24 + 30.25

Combine like terms: 24 + 30.25 = 54.25
30.25 + -11p + p2 = 54.25

Factor a perfect square on the left side:
(p + -5.5)(p + -5.5) = 54.25

Calculate the square root of the right side: 7.365459931

Break this problem into two subproblems by setting 
(p + -5.5) equal to 7.365459931 and -7.365459931.

Subproblem 1

p + -5.5 = 7.365459931 Simplifying p + -5.5 = 7.365459931 Reorder the terms: -5.5 + p = 7.365459931 Solving -5.5 + p = 7.365459931 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + p = 7.365459931 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + p = 7.365459931 + 5.5 p = 7.365459931 + 5.5 Combine like terms: 7.365459931 + 5.5 = 12.865459931 p = 12.865459931 Simplifying p = 12.865459931

Subproblem 2

p + -5.5 = -7.365459931 Simplifying p + -5.5 = -7.365459931 Reorder the terms: -5.5 + p = -7.365459931 Solving -5.5 + p = -7.365459931 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + p = -7.365459931 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + p = -7.365459931 + 5.5 p = -7.365459931 + 5.5 Combine like terms: -7.365459931 + 5.5 = -1.865459931 p = -1.865459931 Simplifying p = -1.865459931

Solution

The solution to the problem is based on the solutions from the subproblems. p = {12.865459931, -1.865459931}

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