(.6p)+(p^2)=.91

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Solution for (.6p)+(p^2)=.91 equation: 


Simplifying
(0.6p) + (p2) = 0.91
(0.6p) + p2 = 0.91

Solving
(0.6p) + p2 = 0.91

Solving for variable 'p'.

Reorder the terms:
-0.91 + (0.6p) + p2 = 0.91 + -0.91

Combine like terms: 0.91 + -0.91 = 0.00
-0.91 + (0.6p) + p2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.91' to each side of the equation.
-0.91 + (0.6p) + 0.91 + p2 = 0.00 + 0.91

Reorder the terms:
-0.91 + 0.91 + (0.6p) + p2 = 0.00 + 0.91

Combine like terms: -0.91 + 0.91 = 0.00
0.00 + (0.6p) + p2 = 0.00 + 0.91
(0.6p) + p2 = 0.00 + 0.91

Combine like terms: 0.00 + 0.91 = 0.91
(0.6p) + p2 = 0.91

The p term is (0.6p).  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
(0.6p) + 0.09 + p2 = 0.91 + 0.09

Reorder the terms:
0.09 + (0.6p) + p2 = 0.91 + 0.09

Combine like terms: 0.91 + 0.09 = 1
0.09 + (0.6p) + p2 = 1

Factor a perfect square on the left side:
(p + 0.3)(p + 0.3) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(p + 0.3) equal to 1 and -1.


Subproblem 1
p + 0.3 = 1

Simplifying
p + 0.3 = 1

Reorder the terms:
0.3 + p = 1

Solving
0.3 + p = 1

Solving for variable 'p'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + p = 1 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + p = 1 + -0.3
p = 1 + -0.3

Combine like terms: 1 + -0.3 = 0.7
p = 0.7

Simplifying
p = 0.7


Subproblem 2
p + 0.3 = -1

Simplifying
p + 0.3 = -1

Reorder the terms:
0.3 + p = -1

Solving
0.3 + p = -1

Solving for variable 'p'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + p = -1 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + p = -1 + -0.3
p = -1 + -0.3

Combine like terms: -1 + -0.3 = -1.3
p = -1.3

Simplifying
p = -1.3


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.7, -1.3}

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