p^2+22p-3=0

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Solution for p^2+22p-3=0 equation:


Simplifying
p2 + 22p + -3 = 0

Reorder the terms:
-3 + 22p + p2 = 0

Solving
-3 + 22p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 22p + 3 + p2 = 0 + 3

Reorder the terms:
-3 + 3 + 22p + p2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 22p + p2 = 0 + 3
22p + p2 = 0 + 3

Combine like terms: 0 + 3 = 3
22p + p2 = 3

The p term is 22p.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22p + 121 + p2 = 3 + 121

Reorder the terms:
121 + 22p + p2 = 3 + 121

Combine like terms: 3 + 121 = 124
121 + 22p + p2 = 124

Factor a perfect square on the left side:
(p + 11)(p + 11) = 124

Calculate the square root of the right side: 11.135528726

Break this problem into two subproblems by setting 
(p + 11) equal to 11.135528726 and -11.135528726.

Subproblem 1

p + 11 = 11.135528726 Simplifying p + 11 = 11.135528726 Reorder the terms: 11 + p = 11.135528726 Solving 11 + p = 11.135528726 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + p = 11.135528726 + -11 Combine like terms: 11 + -11 = 0 0 + p = 11.135528726 + -11 p = 11.135528726 + -11 Combine like terms: 11.135528726 + -11 = 0.135528726 p = 0.135528726 Simplifying p = 0.135528726

Subproblem 2

p + 11 = -11.135528726 Simplifying p + 11 = -11.135528726 Reorder the terms: 11 + p = -11.135528726 Solving 11 + p = -11.135528726 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + p = -11.135528726 + -11 Combine like terms: 11 + -11 = 0 0 + p = -11.135528726 + -11 p = -11.135528726 + -11 Combine like terms: -11.135528726 + -11 = -22.135528726 p = -22.135528726 Simplifying p = -22.135528726

Solution

The solution to the problem is based on the solutions from the subproblems. p = {0.135528726, -22.135528726}

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