p+0.03p*6p=17.70

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Solution for p+0.03p*6p=17.70 equation: 


Simplifying
p + 0.03p * 6p = 17.70

Reorder the terms for easier multiplication:
p + 0.03 * 6p * p = 17.70

Multiply 0.03 * 6
p + 0.18p * p = 17.70

Multiply p * p
p + 0.18p2 = 17.70

Solving
p + 0.18p2 = 17.70

Solving for variable 'p'.

Reorder the terms:
-17.70 + p + 0.18p2 = 17.70 + -17.70

Combine like terms: 17.70 + -17.70 = 0.00
-17.70 + p + 0.18p2 = 0.00

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

Divide each side by '0.18'.
-98.33333333 + 5.555555556p + p2 = 0

Move the constant term to the right:

Add '98.33333333' to each side of the equation.
-98.33333333 + 5.555555556p + 98.33333333 + p2 = 0 + 98.33333333

Reorder the terms:
-98.33333333 + 98.33333333 + 5.555555556p + p2 = 0 + 98.33333333

Combine like terms: -98.33333333 + 98.33333333 = 0.00000000
0.00000000 + 5.555555556p + p2 = 0 + 98.33333333
5.555555556p + p2 = 0 + 98.33333333

Combine like terms: 0 + 98.33333333 = 98.33333333
5.555555556p + p2 = 98.33333333

The p term is p.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
5.555555556p + 0.25 + p2 = 98.33333333 + 0.25

Reorder the terms:
0.25 + 5.555555556p + p2 = 98.33333333 + 0.25

Combine like terms: 98.33333333 + 0.25 = 98.58333333
0.25 + 5.555555556p + p2 = 98.58333333

Factor a perfect square on the left side:
(p + 0.5)(p + 0.5) = 98.58333333

Calculate the square root of the right side: 9.928914006

Break this problem into two subproblems by setting 
(p + 0.5) equal to 9.928914006 and -9.928914006.


Subproblem 1
p + 0.5 = 9.928914006

Simplifying
p + 0.5 = 9.928914006

Reorder the terms:
0.5 + p = 9.928914006

Solving
0.5 + p = 9.928914006

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + p = 9.928914006 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + p = 9.928914006 + -0.5
p = 9.928914006 + -0.5

Combine like terms: 9.928914006 + -0.5 = 9.428914006
p = 9.428914006

Simplifying
p = 9.428914006


Subproblem 2
p + 0.5 = -9.928914006

Simplifying
p + 0.5 = -9.928914006

Reorder the terms:
0.5 + p = -9.928914006

Solving
0.5 + p = -9.928914006

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + p = -9.928914006 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + p = -9.928914006 + -0.5
p = -9.928914006 + -0.5

Combine like terms: -9.928914006 + -0.5 = -10.428914006
p = -10.428914006

Simplifying
p = -10.428914006


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {9.428914006, -10.428914006}

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