7p^2=18p+8

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Solution for 7p^2=18p+8 equation:


Simplifying
7p2 = 18p + 8

Reorder the terms:
7p2 = 8 + 18p

Solving
7p2 = 8 + 18p

Solving for variable 'p'.

Reorder the terms:
-8 + -18p + 7p2 = 8 + 18p + -8 + -18p

Reorder the terms:
-8 + -18p + 7p2 = 8 + -8 + 18p + -18p

Combine like terms: 8 + -8 = 0
-8 + -18p + 7p2 = 0 + 18p + -18p
-8 + -18p + 7p2 = 18p + -18p

Combine like terms: 18p + -18p = 0
-8 + -18p + 7p2 = 0

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

Divide each side by '7'.
-1.142857143 + -2.571428571p + p2 = 0

Move the constant term to the right:

Add '1.142857143' to each side of the equation.
-1.142857143 + -2.571428571p + 1.142857143 + p2 = 0 + 1.142857143

Reorder the terms:
-1.142857143 + 1.142857143 + -2.571428571p + p2 = 0 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + -2.571428571p + p2 = 0 + 1.142857143
-2.571428571p + p2 = 0 + 1.142857143

Combine like terms: 0 + 1.142857143 = 1.142857143
-2.571428571p + p2 = 1.142857143

The p term is -2.571428571p.  Take half its coefficient (-1.285714286).
Square it (1.653061225) and add it to both sides.

Add '1.653061225' to each side of the equation.
-2.571428571p + 1.653061225 + p2 = 1.142857143 + 1.653061225

Reorder the terms:
1.653061225 + -2.571428571p + p2 = 1.142857143 + 1.653061225

Combine like terms: 1.142857143 + 1.653061225 = 2.795918368
1.653061225 + -2.571428571p + p2 = 2.795918368

Factor a perfect square on the left side:
(p + -1.285714286)(p + -1.285714286) = 2.795918368

Calculate the square root of the right side: 1.672099987

Break this problem into two subproblems by setting 
(p + -1.285714286) equal to 1.672099987 and -1.672099987.

Subproblem 1

p + -1.285714286 = 1.672099987 Simplifying p + -1.285714286 = 1.672099987 Reorder the terms: -1.285714286 + p = 1.672099987 Solving -1.285714286 + p = 1.672099987 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.285714286' to each side of the equation. -1.285714286 + 1.285714286 + p = 1.672099987 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + p = 1.672099987 + 1.285714286 p = 1.672099987 + 1.285714286 Combine like terms: 1.672099987 + 1.285714286 = 2.957814273 p = 2.957814273 Simplifying p = 2.957814273

Subproblem 2

p + -1.285714286 = -1.672099987 Simplifying p + -1.285714286 = -1.672099987 Reorder the terms: -1.285714286 + p = -1.672099987 Solving -1.285714286 + p = -1.672099987 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.285714286' to each side of the equation. -1.285714286 + 1.285714286 + p = -1.672099987 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + p = -1.672099987 + 1.285714286 p = -1.672099987 + 1.285714286 Combine like terms: -1.672099987 + 1.285714286 = -0.386385701 p = -0.386385701 Simplifying p = -0.386385701

Solution

The solution to the problem is based on the solutions from the subproblems. p = {2.957814273, -0.386385701}

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