0.25p^2+2p=3

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Solution for 0.25p^2+2p=3 equation:


Simplifying
0.25p2 + 2p = 3

Reorder the terms:
2p + 0.25p2 = 3

Solving
2p + 0.25p2 = 3

Solving for variable 'p'.

Reorder the terms:
-3 + 2p + 0.25p2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 2p + 0.25p2 = 0

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

Divide each side by '0.25'.
-12 + 8p + p2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 8p + 12 + p2 = 0 + 12

Reorder the terms:
-12 + 12 + 8p + p2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 8p + p2 = 0 + 12
8p + p2 = 0 + 12

Combine like terms: 0 + 12 = 12
8p + p2 = 12

The p term is 8p.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8p + 16 + p2 = 12 + 16

Reorder the terms:
16 + 8p + p2 = 12 + 16

Combine like terms: 12 + 16 = 28
16 + 8p + p2 = 28

Factor a perfect square on the left side:
(p + 4)(p + 4) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(p + 4) equal to 5.291502622 and -5.291502622.

Subproblem 1

p + 4 = 5.291502622 Simplifying p + 4 = 5.291502622 Reorder the terms: 4 + p = 5.291502622 Solving 4 + p = 5.291502622 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + p = 5.291502622 + -4 Combine like terms: 4 + -4 = 0 0 + p = 5.291502622 + -4 p = 5.291502622 + -4 Combine like terms: 5.291502622 + -4 = 1.291502622 p = 1.291502622 Simplifying p = 1.291502622

Subproblem 2

p + 4 = -5.291502622 Simplifying p + 4 = -5.291502622 Reorder the terms: 4 + p = -5.291502622 Solving 4 + p = -5.291502622 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + p = -5.291502622 + -4 Combine like terms: 4 + -4 = 0 0 + p = -5.291502622 + -4 p = -5.291502622 + -4 Combine like terms: -5.291502622 + -4 = -9.291502622 p = -9.291502622 Simplifying p = -9.291502622

Solution

The solution to the problem is based on the solutions from the subproblems. p = {1.291502622, -9.291502622}

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