7p(2p+3)-8=6p+29

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Solution for 7p(2p+3)-8=6p+29 equation:


Simplifying
7p(2p + 3) + -8 = 6p + 29

Reorder the terms:
7p(3 + 2p) + -8 = 6p + 29
(3 * 7p + 2p * 7p) + -8 = 6p + 29
(21p + 14p2) + -8 = 6p + 29

Reorder the terms:
-8 + 21p + 14p2 = 6p + 29

Reorder the terms:
-8 + 21p + 14p2 = 29 + 6p

Solving
-8 + 21p + 14p2 = 29 + 6p

Solving for variable 'p'.

Reorder the terms:
-8 + -29 + 21p + -6p + 14p2 = 29 + 6p + -29 + -6p

Combine like terms: -8 + -29 = -37
-37 + 21p + -6p + 14p2 = 29 + 6p + -29 + -6p

Combine like terms: 21p + -6p = 15p
-37 + 15p + 14p2 = 29 + 6p + -29 + -6p

Reorder the terms:
-37 + 15p + 14p2 = 29 + -29 + 6p + -6p

Combine like terms: 29 + -29 = 0
-37 + 15p + 14p2 = 0 + 6p + -6p
-37 + 15p + 14p2 = 6p + -6p

Combine like terms: 6p + -6p = 0
-37 + 15p + 14p2 = 0

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

Divide each side by '14'.
-2.642857143 + 1.071428571p + p2 = 0

Move the constant term to the right:

Add '2.642857143' to each side of the equation.
-2.642857143 + 1.071428571p + 2.642857143 + p2 = 0 + 2.642857143

Reorder the terms:
-2.642857143 + 2.642857143 + 1.071428571p + p2 = 0 + 2.642857143

Combine like terms: -2.642857143 + 2.642857143 = 0.000000000
0.000000000 + 1.071428571p + p2 = 0 + 2.642857143
1.071428571p + p2 = 0 + 2.642857143

Combine like terms: 0 + 2.642857143 = 2.642857143
1.071428571p + p2 = 2.642857143

The p term is 1.071428571p.  Take half its coefficient (0.5357142855).
Square it (0.2869897957) and add it to both sides.

Add '0.2869897957' to each side of the equation.
1.071428571p + 0.2869897957 + p2 = 2.642857143 + 0.2869897957

Reorder the terms:
0.2869897957 + 1.071428571p + p2 = 2.642857143 + 0.2869897957

Combine like terms: 2.642857143 + 0.2869897957 = 2.9298469387
0.2869897957 + 1.071428571p + p2 = 2.9298469387

Factor a perfect square on the left side:
(p + 0.5357142855)(p + 0.5357142855) = 2.9298469387

Calculate the square root of the right side: 1.711679567

Break this problem into two subproblems by setting 
(p + 0.5357142855) equal to 1.711679567 and -1.711679567.

Subproblem 1

p + 0.5357142855 = 1.711679567 Simplifying p + 0.5357142855 = 1.711679567 Reorder the terms: 0.5357142855 + p = 1.711679567 Solving 0.5357142855 + p = 1.711679567 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5357142855' to each side of the equation. 0.5357142855 + -0.5357142855 + p = 1.711679567 + -0.5357142855 Combine like terms: 0.5357142855 + -0.5357142855 = 0.0000000000 0.0000000000 + p = 1.711679567 + -0.5357142855 p = 1.711679567 + -0.5357142855 Combine like terms: 1.711679567 + -0.5357142855 = 1.1759652815 p = 1.1759652815 Simplifying p = 1.1759652815

Subproblem 2

p + 0.5357142855 = -1.711679567 Simplifying p + 0.5357142855 = -1.711679567 Reorder the terms: 0.5357142855 + p = -1.711679567 Solving 0.5357142855 + p = -1.711679567 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5357142855' to each side of the equation. 0.5357142855 + -0.5357142855 + p = -1.711679567 + -0.5357142855 Combine like terms: 0.5357142855 + -0.5357142855 = 0.0000000000 0.0000000000 + p = -1.711679567 + -0.5357142855 p = -1.711679567 + -0.5357142855 Combine like terms: -1.711679567 + -0.5357142855 = -2.2473938525 p = -2.2473938525 Simplifying p = -2.2473938525

Solution

The solution to the problem is based on the solutions from the subproblems. p = {1.1759652815, -2.2473938525}

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