26p^2=60p-25

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Solution for 26p^2=60p-25 equation:


Simplifying
26p2 = 60p + -25

Reorder the terms:
26p2 = -25 + 60p

Solving
26p2 = -25 + 60p

Solving for variable 'p'.

Reorder the terms:
25 + -60p + 26p2 = -25 + 60p + 25 + -60p

Reorder the terms:
25 + -60p + 26p2 = -25 + 25 + 60p + -60p

Combine like terms: -25 + 25 = 0
25 + -60p + 26p2 = 0 + 60p + -60p
25 + -60p + 26p2 = 60p + -60p

Combine like terms: 60p + -60p = 0
25 + -60p + 26p2 = 0

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

Divide each side by '26'.
0.9615384615 + -2.307692308p + p2 = 0

Move the constant term to the right:

Add '-0.9615384615' to each side of the equation.
0.9615384615 + -2.307692308p + -0.9615384615 + p2 = 0 + -0.9615384615

Reorder the terms:
0.9615384615 + -0.9615384615 + -2.307692308p + p2 = 0 + -0.9615384615

Combine like terms: 0.9615384615 + -0.9615384615 = 0.0000000000
0.0000000000 + -2.307692308p + p2 = 0 + -0.9615384615
-2.307692308p + p2 = 0 + -0.9615384615

Combine like terms: 0 + -0.9615384615 = -0.9615384615
-2.307692308p + p2 = -0.9615384615

The p term is -2.307692308p.  Take half its coefficient (-1.153846154).
Square it (1.331360947) and add it to both sides.

Add '1.331360947' to each side of the equation.
-2.307692308p + 1.331360947 + p2 = -0.9615384615 + 1.331360947

Reorder the terms:
1.331360947 + -2.307692308p + p2 = -0.9615384615 + 1.331360947

Combine like terms: -0.9615384615 + 1.331360947 = 0.3698224855
1.331360947 + -2.307692308p + p2 = 0.3698224855

Factor a perfect square on the left side:
(p + -1.153846154)(p + -1.153846154) = 0.3698224855

Calculate the square root of the right side: 0.60813032

Break this problem into two subproblems by setting 
(p + -1.153846154) equal to 0.60813032 and -0.60813032.

Subproblem 1

p + -1.153846154 = 0.60813032 Simplifying p + -1.153846154 = 0.60813032 Reorder the terms: -1.153846154 + p = 0.60813032 Solving -1.153846154 + p = 0.60813032 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.153846154' to each side of the equation. -1.153846154 + 1.153846154 + p = 0.60813032 + 1.153846154 Combine like terms: -1.153846154 + 1.153846154 = 0.000000000 0.000000000 + p = 0.60813032 + 1.153846154 p = 0.60813032 + 1.153846154 Combine like terms: 0.60813032 + 1.153846154 = 1.761976474 p = 1.761976474 Simplifying p = 1.761976474

Subproblem 2

p + -1.153846154 = -0.60813032 Simplifying p + -1.153846154 = -0.60813032 Reorder the terms: -1.153846154 + p = -0.60813032 Solving -1.153846154 + p = -0.60813032 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.153846154' to each side of the equation. -1.153846154 + 1.153846154 + p = -0.60813032 + 1.153846154 Combine like terms: -1.153846154 + 1.153846154 = 0.000000000 0.000000000 + p = -0.60813032 + 1.153846154 p = -0.60813032 + 1.153846154 Combine like terms: -0.60813032 + 1.153846154 = 0.545715834 p = 0.545715834 Simplifying p = 0.545715834

Solution

The solution to the problem is based on the solutions from the subproblems. p = {1.761976474, 0.545715834}

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