7p^2-9p-3=0

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Solution for 7p^2-9p-3=0 equation:


Simplifying
7p2 + -9p + -3 = 0

Reorder the terms:
-3 + -9p + 7p2 = 0

Solving
-3 + -9p + 7p2 = 0

Solving for variable 'p'.

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

Divide each side by '7'.
-0.4285714286 + -1.285714286p + p2 = 0

Move the constant term to the right:

Add '0.4285714286' to each side of the equation.
-0.4285714286 + -1.285714286p + 0.4285714286 + p2 = 0 + 0.4285714286

Reorder the terms:
-0.4285714286 + 0.4285714286 + -1.285714286p + p2 = 0 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + -1.285714286p + p2 = 0 + 0.4285714286
-1.285714286p + p2 = 0 + 0.4285714286

Combine like terms: 0 + 0.4285714286 = 0.4285714286
-1.285714286p + p2 = 0.4285714286

The p term is -1.285714286p.  Take half its coefficient (-0.642857143).
Square it (0.4132653063) and add it to both sides.

Add '0.4132653063' to each side of the equation.
-1.285714286p + 0.4132653063 + p2 = 0.4285714286 + 0.4132653063

Reorder the terms:
0.4132653063 + -1.285714286p + p2 = 0.4285714286 + 0.4132653063

Combine like terms: 0.4285714286 + 0.4132653063 = 0.8418367349
0.4132653063 + -1.285714286p + p2 = 0.8418367349

Factor a perfect square on the left side:
(p + -0.642857143)(p + -0.642857143) = 0.8418367349

Calculate the square root of the right side: 0.917516613

Break this problem into two subproblems by setting 
(p + -0.642857143) equal to 0.917516613 and -0.917516613.

Subproblem 1

p + -0.642857143 = 0.917516613 Simplifying p + -0.642857143 = 0.917516613 Reorder the terms: -0.642857143 + p = 0.917516613 Solving -0.642857143 + p = 0.917516613 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + p = 0.917516613 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + p = 0.917516613 + 0.642857143 p = 0.917516613 + 0.642857143 Combine like terms: 0.917516613 + 0.642857143 = 1.560373756 p = 1.560373756 Simplifying p = 1.560373756

Subproblem 2

p + -0.642857143 = -0.917516613 Simplifying p + -0.642857143 = -0.917516613 Reorder the terms: -0.642857143 + p = -0.917516613 Solving -0.642857143 + p = -0.917516613 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + p = -0.917516613 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + p = -0.917516613 + 0.642857143 p = -0.917516613 + 0.642857143 Combine like terms: -0.917516613 + 0.642857143 = -0.27465947 p = -0.27465947 Simplifying p = -0.27465947

Solution

The solution to the problem is based on the solutions from the subproblems. p = {1.560373756, -0.27465947}

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