8p^2-5p-4=0

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Solution for 8p^2-5p-4=0 equation:


Simplifying
8p2 + -5p + -4 = 0

Reorder the terms:
-4 + -5p + 8p2 = 0

Solving
-4 + -5p + 8p2 = 0

Solving for variable 'p'.

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

Divide each side by '8'.
-0.5 + -0.625p + p2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -0.625p + 0.5 + p2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -0.625p + p2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -0.625p + p2 = 0 + 0.5
-0.625p + p2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-0.625p + p2 = 0.5

The p term is -0.625p.  Take half its coefficient (-0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
-0.625p + 0.09765625 + p2 = 0.5 + 0.09765625

Reorder the terms:
0.09765625 + -0.625p + p2 = 0.5 + 0.09765625

Combine like terms: 0.5 + 0.09765625 = 0.59765625
0.09765625 + -0.625p + p2 = 0.59765625

Factor a perfect square on the left side:
(p + -0.3125)(p + -0.3125) = 0.59765625

Calculate the square root of the right side: 0.773082305

Break this problem into two subproblems by setting 
(p + -0.3125) equal to 0.773082305 and -0.773082305.

Subproblem 1

p + -0.3125 = 0.773082305 Simplifying p + -0.3125 = 0.773082305 Reorder the terms: -0.3125 + p = 0.773082305 Solving -0.3125 + p = 0.773082305 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + p = 0.773082305 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + p = 0.773082305 + 0.3125 p = 0.773082305 + 0.3125 Combine like terms: 0.773082305 + 0.3125 = 1.085582305 p = 1.085582305 Simplifying p = 1.085582305

Subproblem 2

p + -0.3125 = -0.773082305 Simplifying p + -0.3125 = -0.773082305 Reorder the terms: -0.3125 + p = -0.773082305 Solving -0.3125 + p = -0.773082305 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + p = -0.773082305 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + p = -0.773082305 + 0.3125 p = -0.773082305 + 0.3125 Combine like terms: -0.773082305 + 0.3125 = -0.460582305 p = -0.460582305 Simplifying p = -0.460582305

Solution

The solution to the problem is based on the solutions from the subproblems. p = {1.085582305, -0.460582305}

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