p^2+3-2p^2+4p=0

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Solution for p^2+3-2p^2+4p=0 equation:


Simplifying
p2 + 3 + -2p2 + 4p = 0

Reorder the terms:
3 + 4p + p2 + -2p2 = 0

Combine like terms: p2 + -2p2 = -1p2
3 + 4p + -1p2 = 0

Solving
3 + 4p + -1p2 = 0

Solving for variable 'p'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-3 + -4p + p2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -4p + 3 + p2 = 0 + 3

Reorder the terms:
-3 + 3 + -4p + p2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4p + p2 = 0 + 3
-4p + p2 = 0 + 3

Combine like terms: 0 + 3 = 3
-4p + p2 = 3

The p term is -4p.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4p + 4 + p2 = 3 + 4

Reorder the terms:
4 + -4p + p2 = 3 + 4

Combine like terms: 3 + 4 = 7
4 + -4p + p2 = 7

Factor a perfect square on the left side:
(p + -2)(p + -2) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(p + -2) equal to 2.645751311 and -2.645751311.

Subproblem 1

p + -2 = 2.645751311 Simplifying p + -2 = 2.645751311 Reorder the terms: -2 + p = 2.645751311 Solving -2 + p = 2.645751311 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + p = 2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + p = 2.645751311 + 2 p = 2.645751311 + 2 Combine like terms: 2.645751311 + 2 = 4.645751311 p = 4.645751311 Simplifying p = 4.645751311

Subproblem 2

p + -2 = -2.645751311 Simplifying p + -2 = -2.645751311 Reorder the terms: -2 + p = -2.645751311 Solving -2 + p = -2.645751311 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + p = -2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + p = -2.645751311 + 2 p = -2.645751311 + 2 Combine like terms: -2.645751311 + 2 = -0.645751311 p = -0.645751311 Simplifying p = -0.645751311

Solution

The solution to the problem is based on the solutions from the subproblems. p = {4.645751311, -0.645751311}

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