5p^2-6p-3=0

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Solution for 5p^2-6p-3=0 equation:


Simplifying
5p2 + -6p + -3 = 0

Reorder the terms:
-3 + -6p + 5p2 = 0

Solving
-3 + -6p + 5p2 = 0

Solving for variable 'p'.

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

Divide each side by '5'.
-0.6 + -1.2p + p2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -1.2p + 0.6 + p2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -1.2p + p2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -1.2p + p2 = 0 + 0.6
-1.2p + p2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-1.2p + p2 = 0.6

The p term is -1.2p.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2p + 0.36 + p2 = 0.6 + 0.36

Reorder the terms:
0.36 + -1.2p + p2 = 0.6 + 0.36

Combine like terms: 0.6 + 0.36 = 0.96
0.36 + -1.2p + p2 = 0.96

Factor a perfect square on the left side:
(p + -0.6)(p + -0.6) = 0.96

Calculate the square root of the right side: 0.979795897

Break this problem into two subproblems by setting 
(p + -0.6) equal to 0.979795897 and -0.979795897.

Subproblem 1

p + -0.6 = 0.979795897 Simplifying p + -0.6 = 0.979795897 Reorder the terms: -0.6 + p = 0.979795897 Solving -0.6 + p = 0.979795897 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + p = 0.979795897 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + p = 0.979795897 + 0.6 p = 0.979795897 + 0.6 Combine like terms: 0.979795897 + 0.6 = 1.579795897 p = 1.579795897 Simplifying p = 1.579795897

Subproblem 2

p + -0.6 = -0.979795897 Simplifying p + -0.6 = -0.979795897 Reorder the terms: -0.6 + p = -0.979795897 Solving -0.6 + p = -0.979795897 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + p = -0.979795897 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + p = -0.979795897 + 0.6 p = -0.979795897 + 0.6 Combine like terms: -0.979795897 + 0.6 = -0.379795897 p = -0.379795897 Simplifying p = -0.379795897

Solution

The solution to the problem is based on the solutions from the subproblems. p = {1.579795897, -0.379795897}

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