-8+4p^2+1p=0

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Solution for -8+4p^2+1p=0 equation:


Simplifying
-8 + 4p2 + 1p = 0

Reorder the terms:
-8 + 1p + 4p2 = 0

Solving
-8 + 1p + 4p2 = 0

Solving for variable 'p'.

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

Divide each side by '4'.
-2 + 0.25p + p2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 0.25p + 2 + p2 = 0 + 2

Reorder the terms:
-2 + 2 + 0.25p + p2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 0.25p + p2 = 0 + 2
0.25p + p2 = 0 + 2

Combine like terms: 0 + 2 = 2
0.25p + p2 = 2

The p term is 0.25p.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25p + 0.015625 + p2 = 2 + 0.015625

Reorder the terms:
0.015625 + 0.25p + p2 = 2 + 0.015625

Combine like terms: 2 + 0.015625 = 2.015625
0.015625 + 0.25p + p2 = 2.015625

Factor a perfect square on the left side:
(p + 0.125)(p + 0.125) = 2.015625

Calculate the square root of the right side: 1.419727086

Break this problem into two subproblems by setting 
(p + 0.125) equal to 1.419727086 and -1.419727086.

Subproblem 1

p + 0.125 = 1.419727086 Simplifying p + 0.125 = 1.419727086 Reorder the terms: 0.125 + p = 1.419727086 Solving 0.125 + p = 1.419727086 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + p = 1.419727086 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + p = 1.419727086 + -0.125 p = 1.419727086 + -0.125 Combine like terms: 1.419727086 + -0.125 = 1.294727086 p = 1.294727086 Simplifying p = 1.294727086

Subproblem 2

p + 0.125 = -1.419727086 Simplifying p + 0.125 = -1.419727086 Reorder the terms: 0.125 + p = -1.419727086 Solving 0.125 + p = -1.419727086 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + p = -1.419727086 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + p = -1.419727086 + -0.125 p = -1.419727086 + -0.125 Combine like terms: -1.419727086 + -0.125 = -1.544727086 p = -1.544727086 Simplifying p = -1.544727086

Solution

The solution to the problem is based on the solutions from the subproblems. p = {1.294727086, -1.544727086}

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