49(p)(p)-64p+12=0

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Solution for 49(p)(p)-64p+12=0 equation:


Simplifying
49(p)(p) + -64p + 12 = 0

Multiply p * p
49p2 + -64p + 12 = 0

Reorder the terms:
12 + -64p + 49p2 = 0

Solving
12 + -64p + 49p2 = 0

Solving for variable 'p'.

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

Divide each side by '49'.
0.2448979592 + -1.306122449p + p2 = 0

Move the constant term to the right:

Add '-0.2448979592' to each side of the equation.
0.2448979592 + -1.306122449p + -0.2448979592 + p2 = 0 + -0.2448979592

Reorder the terms:
0.2448979592 + -0.2448979592 + -1.306122449p + p2 = 0 + -0.2448979592

Combine like terms: 0.2448979592 + -0.2448979592 = 0.0000000000
0.0000000000 + -1.306122449p + p2 = 0 + -0.2448979592
-1.306122449p + p2 = 0 + -0.2448979592

Combine like terms: 0 + -0.2448979592 = -0.2448979592
-1.306122449p + p2 = -0.2448979592

The p term is -1.306122449p.  Take half its coefficient (-0.6530612245).
Square it (0.4264889629) and add it to both sides.

Add '0.4264889629' to each side of the equation.
-1.306122449p + 0.4264889629 + p2 = -0.2448979592 + 0.4264889629

Reorder the terms:
0.4264889629 + -1.306122449p + p2 = -0.2448979592 + 0.4264889629

Combine like terms: -0.2448979592 + 0.4264889629 = 0.1815910037
0.4264889629 + -1.306122449p + p2 = 0.1815910037

Factor a perfect square on the left side:
(p + -0.6530612245)(p + -0.6530612245) = 0.1815910037

Calculate the square root of the right side: 0.426134959

Break this problem into two subproblems by setting 
(p + -0.6530612245) equal to 0.426134959 and -0.426134959.

Subproblem 1

p + -0.6530612245 = 0.426134959 Simplifying p + -0.6530612245 = 0.426134959 Reorder the terms: -0.6530612245 + p = 0.426134959 Solving -0.6530612245 + p = 0.426134959 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.6530612245' to each side of the equation. -0.6530612245 + 0.6530612245 + p = 0.426134959 + 0.6530612245 Combine like terms: -0.6530612245 + 0.6530612245 = 0.0000000000 0.0000000000 + p = 0.426134959 + 0.6530612245 p = 0.426134959 + 0.6530612245 Combine like terms: 0.426134959 + 0.6530612245 = 1.0791961835 p = 1.0791961835 Simplifying p = 1.0791961835

Subproblem 2

p + -0.6530612245 = -0.426134959 Simplifying p + -0.6530612245 = -0.426134959 Reorder the terms: -0.6530612245 + p = -0.426134959 Solving -0.6530612245 + p = -0.426134959 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.6530612245' to each side of the equation. -0.6530612245 + 0.6530612245 + p = -0.426134959 + 0.6530612245 Combine like terms: -0.6530612245 + 0.6530612245 = 0.0000000000 0.0000000000 + p = -0.426134959 + 0.6530612245 p = -0.426134959 + 0.6530612245 Combine like terms: -0.426134959 + 0.6530612245 = 0.2269262655 p = 0.2269262655 Simplifying p = 0.2269262655

Solution

The solution to the problem is based on the solutions from the subproblems. p = {1.0791961835, 0.2269262655}

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