-p^2+98(p)-200=0

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Solution for -p^2+98(p)-200=0 equation:


Simplifying
-1p2 + 98(p) + -200 = 0

Reorder the terms:
-200 + 98p + -1p2 = 0

Solving
-200 + 98p + -1p2 = 0

Solving for variable 'p'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
200 + -98p + p2 = 0

Move the constant term to the right:

Add '-200' to each side of the equation.
200 + -98p + -200 + p2 = 0 + -200

Reorder the terms:
200 + -200 + -98p + p2 = 0 + -200

Combine like terms: 200 + -200 = 0
0 + -98p + p2 = 0 + -200
-98p + p2 = 0 + -200

Combine like terms: 0 + -200 = -200
-98p + p2 = -200

The p term is -98p.  Take half its coefficient (-49).
Square it (2401) and add it to both sides.

Add '2401' to each side of the equation.
-98p + 2401 + p2 = -200 + 2401

Reorder the terms:
2401 + -98p + p2 = -200 + 2401

Combine like terms: -200 + 2401 = 2201
2401 + -98p + p2 = 2201

Factor a perfect square on the left side:
(p + -49)(p + -49) = 2201

Calculate the square root of the right side: 46.914816423

Break this problem into two subproblems by setting 
(p + -49) equal to 46.914816423 and -46.914816423.

Subproblem 1

p + -49 = 46.914816423 Simplifying p + -49 = 46.914816423 Reorder the terms: -49 + p = 46.914816423 Solving -49 + p = 46.914816423 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '49' to each side of the equation. -49 + 49 + p = 46.914816423 + 49 Combine like terms: -49 + 49 = 0 0 + p = 46.914816423 + 49 p = 46.914816423 + 49 Combine like terms: 46.914816423 + 49 = 95.914816423 p = 95.914816423 Simplifying p = 95.914816423

Subproblem 2

p + -49 = -46.914816423 Simplifying p + -49 = -46.914816423 Reorder the terms: -49 + p = -46.914816423 Solving -49 + p = -46.914816423 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '49' to each side of the equation. -49 + 49 + p = -46.914816423 + 49 Combine like terms: -49 + 49 = 0 0 + p = -46.914816423 + 49 p = -46.914816423 + 49 Combine like terms: -46.914816423 + 49 = 2.085183577 p = 2.085183577 Simplifying p = 2.085183577

Solution

The solution to the problem is based on the solutions from the subproblems. p = {95.914816423, 2.085183577}

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