2p^2+6p=5

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Solution for 2p^2+6p=5 equation:


Simplifying
2p2 + 6p = 5

Reorder the terms:
6p + 2p2 = 5

Solving
6p + 2p2 = 5

Solving for variable 'p'.

Reorder the terms:
-5 + 6p + 2p2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 6p + 2p2 = 0

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

Divide each side by '2'.
-2.5 + 3p + p2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 3p + 2.5 + p2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 3p + p2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 3p + p2 = 0 + 2.5
3p + p2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
3p + p2 = 2.5

The p term is 3p.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3p + 2.25 + p2 = 2.5 + 2.25

Reorder the terms:
2.25 + 3p + p2 = 2.5 + 2.25

Combine like terms: 2.5 + 2.25 = 4.75
2.25 + 3p + p2 = 4.75

Factor a perfect square on the left side:
(p + 1.5)(p + 1.5) = 4.75

Calculate the square root of the right side: 2.179449472

Break this problem into two subproblems by setting 
(p + 1.5) equal to 2.179449472 and -2.179449472.

Subproblem 1

p + 1.5 = 2.179449472 Simplifying p + 1.5 = 2.179449472 Reorder the terms: 1.5 + p = 2.179449472 Solving 1.5 + p = 2.179449472 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + p = 2.179449472 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + p = 2.179449472 + -1.5 p = 2.179449472 + -1.5 Combine like terms: 2.179449472 + -1.5 = 0.679449472 p = 0.679449472 Simplifying p = 0.679449472

Subproblem 2

p + 1.5 = -2.179449472 Simplifying p + 1.5 = -2.179449472 Reorder the terms: 1.5 + p = -2.179449472 Solving 1.5 + p = -2.179449472 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + p = -2.179449472 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + p = -2.179449472 + -1.5 p = -2.179449472 + -1.5 Combine like terms: -2.179449472 + -1.5 = -3.679449472 p = -3.679449472 Simplifying p = -3.679449472

Solution

The solution to the problem is based on the solutions from the subproblems. p = {0.679449472, -3.679449472}

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