P^2+20P-9=-7

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Solution for P^2+20P-9=-7 equation:


Simplifying
P2 + 20P + -9 = -7

Reorder the terms:
-9 + 20P + P2 = -7

Solving
-9 + 20P + P2 = -7

Solving for variable 'P'.

Reorder the terms:
-9 + 7 + 20P + P2 = -7 + 7

Combine like terms: -9 + 7 = -2
-2 + 20P + P2 = -7 + 7

Combine like terms: -7 + 7 = 0
-2 + 20P + P2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 20P + 2 + P2 = 0 + 2

Reorder the terms:
-2 + 2 + 20P + P2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 20P + P2 = 0 + 2
20P + P2 = 0 + 2

Combine like terms: 0 + 2 = 2
20P + P2 = 2

The P term is 20P.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20P + 100 + P2 = 2 + 100

Reorder the terms:
100 + 20P + P2 = 2 + 100

Combine like terms: 2 + 100 = 102
100 + 20P + P2 = 102

Factor a perfect square on the left side:
(P + 10)(P + 10) = 102

Calculate the square root of the right side: 10.099504938

Break this problem into two subproblems by setting 
(P + 10) equal to 10.099504938 and -10.099504938.

Subproblem 1

P + 10 = 10.099504938 Simplifying P + 10 = 10.099504938 Reorder the terms: 10 + P = 10.099504938 Solving 10 + P = 10.099504938 Solving for variable 'P'. Move all terms containing P to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + P = 10.099504938 + -10 Combine like terms: 10 + -10 = 0 0 + P = 10.099504938 + -10 P = 10.099504938 + -10 Combine like terms: 10.099504938 + -10 = 0.099504938 P = 0.099504938 Simplifying P = 0.099504938

Subproblem 2

P + 10 = -10.099504938 Simplifying P + 10 = -10.099504938 Reorder the terms: 10 + P = -10.099504938 Solving 10 + P = -10.099504938 Solving for variable 'P'. Move all terms containing P to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + P = -10.099504938 + -10 Combine like terms: 10 + -10 = 0 0 + P = -10.099504938 + -10 P = -10.099504938 + -10 Combine like terms: -10.099504938 + -10 = -20.099504938 P = -20.099504938 Simplifying P = -20.099504938

Solution

The solution to the problem is based on the solutions from the subproblems. P = {0.099504938, -20.099504938}

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