p^2+2p(.16)+.0256=1

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Solution for p^2+2p(.16)+.0256=1 equation: 


Simplifying
p2 + 2p(0.16) + 0.0256 = 1

Reorder the terms for easier multiplication:
p2 + 2 * 0.16p + 0.0256 = 1

Multiply 2 * 0.16
p2 + 0.32p + 0.0256 = 1

Reorder the terms:
0.0256 + 0.32p + p2 = 1

Solving
0.0256 + 0.32p + p2 = 1

Solving for variable 'p'.

Reorder the terms:
0.0256 + -1 + 0.32p + p2 = 1 + -1

Combine like terms: 0.0256 + -1 = -0.9744
-0.9744 + 0.32p + p2 = 1 + -1

Combine like terms: 1 + -1 = 0
-0.9744 + 0.32p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '0.9744' to each side of the equation.
-0.9744 + 0.32p + 0.9744 + p2 = 0 + 0.9744

Reorder the terms:
-0.9744 + 0.9744 + 0.32p + p2 = 0 + 0.9744

Combine like terms: -0.9744 + 0.9744 = 0.0000
0.0000 + 0.32p + p2 = 0 + 0.9744
0.32p + p2 = 0 + 0.9744

Combine like terms: 0 + 0.9744 = 0.9744
0.32p + p2 = 0.9744

The p term is 0.32p.  Take half its coefficient (0.16).
Square it (0.0256) and add it to both sides.

Add '0.0256' to each side of the equation.
0.32p + 0.0256 + p2 = 0.9744 + 0.0256

Reorder the terms:
0.0256 + 0.32p + p2 = 0.9744 + 0.0256

Combine like terms: 0.9744 + 0.0256 = 1
0.0256 + 0.32p + p2 = 1

Factor a perfect square on the left side:
(p + 0.16)(p + 0.16) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(p + 0.16) equal to 1 and -1.


Subproblem 1
p + 0.16 = 1

Simplifying
p + 0.16 = 1

Reorder the terms:
0.16 + p = 1

Solving
0.16 + p = 1

Solving for variable 'p'.

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

Add '-0.16' to each side of the equation.
0.16 + -0.16 + p = 1 + -0.16

Combine like terms: 0.16 + -0.16 = 0.00
0.00 + p = 1 + -0.16
p = 1 + -0.16

Combine like terms: 1 + -0.16 = 0.84
p = 0.84

Simplifying
p = 0.84


Subproblem 2
p + 0.16 = -1

Simplifying
p + 0.16 = -1

Reorder the terms:
0.16 + p = -1

Solving
0.16 + p = -1

Solving for variable 'p'.

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

Add '-0.16' to each side of the equation.
0.16 + -0.16 + p = -1 + -0.16

Combine like terms: 0.16 + -0.16 = 0.00
0.00 + p = -1 + -0.16
p = -1 + -0.16

Combine like terms: -1 + -0.16 = -1.16
p = -1.16

Simplifying
p = -1.16


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.84, -1.16}

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