7p^2+5=16p

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Solution for 7p^2+5=16p equation:


Simplifying
7p2 + 5 = 16p

Reorder the terms:
5 + 7p2 = 16p

Solving
5 + 7p2 = 16p

Solving for variable 'p'.

Reorder the terms:
5 + -16p + 7p2 = 16p + -16p

Combine like terms: 16p + -16p = 0
5 + -16p + 7p2 = 0

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

Divide each side by '7'.
0.7142857143 + -2.285714286p + p2 = 0

Move the constant term to the right:

Add '-0.7142857143' to each side of the equation.
0.7142857143 + -2.285714286p + -0.7142857143 + p2 = 0 + -0.7142857143

Reorder the terms:
0.7142857143 + -0.7142857143 + -2.285714286p + p2 = 0 + -0.7142857143

Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000
0.0000000000 + -2.285714286p + p2 = 0 + -0.7142857143
-2.285714286p + p2 = 0 + -0.7142857143

Combine like terms: 0 + -0.7142857143 = -0.7142857143
-2.285714286p + p2 = -0.7142857143

The p term is -2.285714286p.  Take half its coefficient (-1.142857143).
Square it (1.306122449) and add it to both sides.

Add '1.306122449' to each side of the equation.
-2.285714286p + 1.306122449 + p2 = -0.7142857143 + 1.306122449

Reorder the terms:
1.306122449 + -2.285714286p + p2 = -0.7142857143 + 1.306122449

Combine like terms: -0.7142857143 + 1.306122449 = 0.5918367347
1.306122449 + -2.285714286p + p2 = 0.5918367347

Factor a perfect square on the left side:
(p + -1.142857143)(p + -1.142857143) = 0.5918367347

Calculate the square root of the right side: 0.769309258

Break this problem into two subproblems by setting 
(p + -1.142857143) equal to 0.769309258 and -0.769309258.

Subproblem 1

p + -1.142857143 = 0.769309258 Simplifying p + -1.142857143 = 0.769309258 Reorder the terms: -1.142857143 + p = 0.769309258 Solving -1.142857143 + p = 0.769309258 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + p = 0.769309258 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + p = 0.769309258 + 1.142857143 p = 0.769309258 + 1.142857143 Combine like terms: 0.769309258 + 1.142857143 = 1.912166401 p = 1.912166401 Simplifying p = 1.912166401

Subproblem 2

p + -1.142857143 = -0.769309258 Simplifying p + -1.142857143 = -0.769309258 Reorder the terms: -1.142857143 + p = -0.769309258 Solving -1.142857143 + p = -0.769309258 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + p = -0.769309258 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + p = -0.769309258 + 1.142857143 p = -0.769309258 + 1.142857143 Combine like terms: -0.769309258 + 1.142857143 = 0.373547885 p = 0.373547885 Simplifying p = 0.373547885

Solution

The solution to the problem is based on the solutions from the subproblems. p = {1.912166401, 0.373547885}

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