26p^2+60p-25=

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


Simplifying
26p2 + 60p + -25 = 0

Reorder the terms:
-25 + 60p + 26p2 = 0

Solving
-25 + 60p + 26p2 = 0

Solving for variable 'p'.

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 = 2.2928994085
1.331360947 + 2.307692308p + p2 = 2.2928994085

Factor a perfect square on the left side:
(p + 1.153846154)(p + 1.153846154) = 2.2928994085

Calculate the square root of the right side: 1.514232284

Break this problem into two subproblems by setting 
(p + 1.153846154) equal to 1.514232284 and -1.514232284.

Subproblem 1

p + 1.153846154 = 1.514232284 Simplifying p + 1.153846154 = 1.514232284 Reorder the terms: 1.153846154 + p = 1.514232284 Solving 1.153846154 + p = 1.514232284 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 = 1.514232284 + -1.153846154 Combine like terms: 1.153846154 + -1.153846154 = 0.000000000 0.000000000 + p = 1.514232284 + -1.153846154 p = 1.514232284 + -1.153846154 Combine like terms: 1.514232284 + -1.153846154 = 0.36038613 p = 0.36038613 Simplifying p = 0.36038613

Subproblem 2

p + 1.153846154 = -1.514232284 Simplifying p + 1.153846154 = -1.514232284 Reorder the terms: 1.153846154 + p = -1.514232284 Solving 1.153846154 + p = -1.514232284 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 = -1.514232284 + -1.153846154 Combine like terms: 1.153846154 + -1.153846154 = 0.000000000 0.000000000 + p = -1.514232284 + -1.153846154 p = -1.514232284 + -1.153846154 Combine like terms: -1.514232284 + -1.153846154 = -2.668078438 p = -2.668078438 Simplifying p = -2.668078438

Solution

The solution to the problem is based on the solutions from the subproblems. p = {0.36038613, -2.668078438}

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