2p^2-29p=6

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Solution for 2p^2-29p=6 equation:


Simplifying
2p2 + -29p = 6

Reorder the terms:
-29p + 2p2 = 6

Solving
-29p + 2p2 = 6

Solving for variable 'p'.

Reorder the terms:
-6 + -29p + 2p2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -29p + 2p2 = 0

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

Divide each side by '2'.
-3 + -14.5p + p2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -14.5p + 3 + p2 = 0 + 3

Reorder the terms:
-3 + 3 + -14.5p + p2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -14.5p + p2 = 0 + 3
-14.5p + p2 = 0 + 3

Combine like terms: 0 + 3 = 3
-14.5p + p2 = 3

The p term is -14.5p.  Take half its coefficient (-7.25).
Square it (52.5625) and add it to both sides.

Add '52.5625' to each side of the equation.
-14.5p + 52.5625 + p2 = 3 + 52.5625

Reorder the terms:
52.5625 + -14.5p + p2 = 3 + 52.5625

Combine like terms: 3 + 52.5625 = 55.5625
52.5625 + -14.5p + p2 = 55.5625

Factor a perfect square on the left side:
(p + -7.25)(p + -7.25) = 55.5625

Calculate the square root of the right side: 7.454025758

Break this problem into two subproblems by setting 
(p + -7.25) equal to 7.454025758 and -7.454025758.

Subproblem 1

p + -7.25 = 7.454025758 Simplifying p + -7.25 = 7.454025758 Reorder the terms: -7.25 + p = 7.454025758 Solving -7.25 + p = 7.454025758 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '7.25' to each side of the equation. -7.25 + 7.25 + p = 7.454025758 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + p = 7.454025758 + 7.25 p = 7.454025758 + 7.25 Combine like terms: 7.454025758 + 7.25 = 14.704025758 p = 14.704025758 Simplifying p = 14.704025758

Subproblem 2

p + -7.25 = -7.454025758 Simplifying p + -7.25 = -7.454025758 Reorder the terms: -7.25 + p = -7.454025758 Solving -7.25 + p = -7.454025758 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '7.25' to each side of the equation. -7.25 + 7.25 + p = -7.454025758 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + p = -7.454025758 + 7.25 p = -7.454025758 + 7.25 Combine like terms: -7.454025758 + 7.25 = -0.204025758 p = -0.204025758 Simplifying p = -0.204025758

Solution

The solution to the problem is based on the solutions from the subproblems. p = {14.704025758, -0.204025758}

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