2.14p^2-7.74p=5.71

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Solution for 2.14p^2-7.74p=5.71 equation:


Simplifying
2.14p2 + -7.74p = 5.71

Reorder the terms:
-7.74p + 2.14p2 = 5.71

Solving
-7.74p + 2.14p2 = 5.71

Solving for variable 'p'.

Reorder the terms:
-5.71 + -7.74p + 2.14p2 = 5.71 + -5.71

Combine like terms: 5.71 + -5.71 = 0.00
-5.71 + -7.74p + 2.14p2 = 0.00

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

Divide each side by '2.14'.
-2.668224299 + -3.61682243p + p2 = 0

Move the constant term to the right:

Add '2.668224299' to each side of the equation.
-2.668224299 + -3.61682243p + 2.668224299 + p2 = 0 + 2.668224299

Reorder the terms:
-2.668224299 + 2.668224299 + -3.61682243p + p2 = 0 + 2.668224299

Combine like terms: -2.668224299 + 2.668224299 = 0.000000000
0.000000000 + -3.61682243p + p2 = 0 + 2.668224299
-3.61682243p + p2 = 0 + 2.668224299

Combine like terms: 0 + 2.668224299 = 2.668224299
-3.61682243p + p2 = 2.668224299

The p term is -3.61682243p.  Take half its coefficient (-1.808411215).
Square it (3.270351123) and add it to both sides.

Add '3.270351123' to each side of the equation.
-3.61682243p + 3.270351123 + p2 = 2.668224299 + 3.270351123

Reorder the terms:
3.270351123 + -3.61682243p + p2 = 2.668224299 + 3.270351123

Combine like terms: 2.668224299 + 3.270351123 = 5.938575422
3.270351123 + -3.61682243p + p2 = 5.938575422

Factor a perfect square on the left side:
(p + -1.808411215)(p + -1.808411215) = 5.938575422

Calculate the square root of the right side: 2.436919248

Break this problem into two subproblems by setting 
(p + -1.808411215) equal to 2.436919248 and -2.436919248.

Subproblem 1

p + -1.808411215 = 2.436919248 Simplifying p + -1.808411215 = 2.436919248 Reorder the terms: -1.808411215 + p = 2.436919248 Solving -1.808411215 + p = 2.436919248 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.808411215' to each side of the equation. -1.808411215 + 1.808411215 + p = 2.436919248 + 1.808411215 Combine like terms: -1.808411215 + 1.808411215 = 0.000000000 0.000000000 + p = 2.436919248 + 1.808411215 p = 2.436919248 + 1.808411215 Combine like terms: 2.436919248 + 1.808411215 = 4.245330463 p = 4.245330463 Simplifying p = 4.245330463

Subproblem 2

p + -1.808411215 = -2.436919248 Simplifying p + -1.808411215 = -2.436919248 Reorder the terms: -1.808411215 + p = -2.436919248 Solving -1.808411215 + p = -2.436919248 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.808411215' to each side of the equation. -1.808411215 + 1.808411215 + p = -2.436919248 + 1.808411215 Combine like terms: -1.808411215 + 1.808411215 = 0.000000000 0.000000000 + p = -2.436919248 + 1.808411215 p = -2.436919248 + 1.808411215 Combine like terms: -2.436919248 + 1.808411215 = -0.628508033 p = -0.628508033 Simplifying p = -0.628508033

Solution

The solution to the problem is based on the solutions from the subproblems. p = {4.245330463, -0.628508033}

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