3p^2-3p-11=0

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Solution for 3p^2-3p-11=0 equation:


Simplifying
3p2 + -3p + -11 = 0

Reorder the terms:
-11 + -3p + 3p2 = 0

Solving
-11 + -3p + 3p2 = 0

Solving for variable 'p'.

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

Divide each side by '3'.
-3.666666667 + -1p + p2 = 0

Move the constant term to the right:

Add '3.666666667' to each side of the equation.
-3.666666667 + -1p + 3.666666667 + p2 = 0 + 3.666666667

Reorder the terms:
-3.666666667 + 3.666666667 + -1p + p2 = 0 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + -1p + p2 = 0 + 3.666666667
-1p + p2 = 0 + 3.666666667

Combine like terms: 0 + 3.666666667 = 3.666666667
-1p + p2 = 3.666666667

The p term is -1p.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1p + 0.25 + p2 = 3.666666667 + 0.25

Reorder the terms:
0.25 + -1p + p2 = 3.666666667 + 0.25

Combine like terms: 3.666666667 + 0.25 = 3.916666667
0.25 + -1p + p2 = 3.916666667

Factor a perfect square on the left side:
(p + -0.5)(p + -0.5) = 3.916666667

Calculate the square root of the right side: 1.979057015

Break this problem into two subproblems by setting 
(p + -0.5) equal to 1.979057015 and -1.979057015.

Subproblem 1

p + -0.5 = 1.979057015 Simplifying p + -0.5 = 1.979057015 Reorder the terms: -0.5 + p = 1.979057015 Solving -0.5 + p = 1.979057015 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + p = 1.979057015 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + p = 1.979057015 + 0.5 p = 1.979057015 + 0.5 Combine like terms: 1.979057015 + 0.5 = 2.479057015 p = 2.479057015 Simplifying p = 2.479057015

Subproblem 2

p + -0.5 = -1.979057015 Simplifying p + -0.5 = -1.979057015 Reorder the terms: -0.5 + p = -1.979057015 Solving -0.5 + p = -1.979057015 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + p = -1.979057015 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + p = -1.979057015 + 0.5 p = -1.979057015 + 0.5 Combine like terms: -1.979057015 + 0.5 = -1.479057015 p = -1.479057015 Simplifying p = -1.479057015

Solution

The solution to the problem is based on the solutions from the subproblems. p = {2.479057015, -1.479057015}

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