p^2+(2p*0.583)+.34=1

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Solution for p^2+(2p*0.583)+.34=1 equation: 


Simplifying
p2 + (2p * 0.583) + 0.34 = 1

Reorder the terms for easier multiplication:
p2 + (2 * 0.583p) + 0.34 = 1

Multiply 2 * 0.583
p2 + (1.166p) + 0.34 = 1

Reorder the terms:
0.34 + (1.166p) + p2 = 1

Solving
0.34 + (1.166p) + p2 = 1

Solving for variable 'p'.

Reorder the terms:
0.34 + -1 + (1.166p) + p2 = 1 + -1

Combine like terms: 0.34 + -1 = -0.66
-0.66 + (1.166p) + p2 = 1 + -1

Combine like terms: 1 + -1 = 0
-0.66 + (1.166p) + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '0.66' to each side of the equation.
-0.66 + (1.166p) + 0.66 + p2 = 0 + 0.66

Reorder the terms:
-0.66 + 0.66 + (1.166p) + p2 = 0 + 0.66

Combine like terms: -0.66 + 0.66 = 0.00
0.00 + (1.166p) + p2 = 0 + 0.66
(1.166p) + p2 = 0 + 0.66

Combine like terms: 0 + 0.66 = 0.66
(1.166p) + p2 = 0.66

The p term is (1.166p).  Take half its coefficient (0.583).
Square it (0.339889) and add it to both sides.

Add '0.339889' to each side of the equation.
(1.166p) + 0.339889 + p2 = 0.66 + 0.339889

Reorder the terms:
0.339889 + (1.166p) + p2 = 0.66 + 0.339889

Combine like terms: 0.66 + 0.339889 = 0.999889
0.339889 + (1.166p) + p2 = 0.999889

Factor a perfect square on the left side:
(p + 0.583)(p + 0.583) = 0.999889

Calculate the square root of the right side: 0.999944498

Break this problem into two subproblems by setting 
(p + 0.583) equal to 0.999944498 and -0.999944498.


Subproblem 1
p + 0.583 = 0.999944498

Simplifying
p + 0.583 = 0.999944498

Reorder the terms:
0.583 + p = 0.999944498

Solving
0.583 + p = 0.999944498

Solving for variable 'p'.

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

Add '-0.583' to each side of the equation.
0.583 + -0.583 + p = 0.999944498 + -0.583

Combine like terms: 0.583 + -0.583 = 0.000
0.000 + p = 0.999944498 + -0.583
p = 0.999944498 + -0.583

Combine like terms: 0.999944498 + -0.583 = 0.416944498
p = 0.416944498

Simplifying
p = 0.416944498


Subproblem 2
p + 0.583 = -0.999944498

Simplifying
p + 0.583 = -0.999944498

Reorder the terms:
0.583 + p = -0.999944498

Solving
0.583 + p = -0.999944498

Solving for variable 'p'.

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

Add '-0.583' to each side of the equation.
0.583 + -0.583 + p = -0.999944498 + -0.583

Combine like terms: 0.583 + -0.583 = 0.000
0.000 + p = -0.999944498 + -0.583
p = -0.999944498 + -0.583

Combine like terms: -0.999944498 + -0.583 = -1.582944498
p = -1.582944498

Simplifying
p = -1.582944498


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.416944498, -1.582944498}

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