21p^2+30p-40=0

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Solution for 21p^2+30p-40=0 equation:


Simplifying
21p2 + 30p + -40 = 0

Reorder the terms:
-40 + 30p + 21p2 = 0

Solving
-40 + 30p + 21p2 = 0

Solving for variable 'p'.

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

Divide each side by '21'.
-1.904761905 + 1.428571429p + p2 = 0

Move the constant term to the right:

Add '1.904761905' to each side of the equation.
-1.904761905 + 1.428571429p + 1.904761905 + p2 = 0 + 1.904761905

Reorder the terms:
-1.904761905 + 1.904761905 + 1.428571429p + p2 = 0 + 1.904761905

Combine like terms: -1.904761905 + 1.904761905 = 0.000000000
0.000000000 + 1.428571429p + p2 = 0 + 1.904761905
1.428571429p + p2 = 0 + 1.904761905

Combine like terms: 0 + 1.904761905 = 1.904761905
1.428571429p + p2 = 1.904761905

The p term is 1.428571429p.  Take half its coefficient (0.7142857145).
Square it (0.5102040819) and add it to both sides.

Add '0.5102040819' to each side of the equation.
1.428571429p + 0.5102040819 + p2 = 1.904761905 + 0.5102040819

Reorder the terms:
0.5102040819 + 1.428571429p + p2 = 1.904761905 + 0.5102040819

Combine like terms: 1.904761905 + 0.5102040819 = 2.4149659869
0.5102040819 + 1.428571429p + p2 = 2.4149659869

Factor a perfect square on the left side:
(p + 0.7142857145)(p + 0.7142857145) = 2.4149659869

Calculate the square root of the right side: 1.554016083

Break this problem into two subproblems by setting 
(p + 0.7142857145) equal to 1.554016083 and -1.554016083.

Subproblem 1

p + 0.7142857145 = 1.554016083 Simplifying p + 0.7142857145 = 1.554016083 Reorder the terms: 0.7142857145 + p = 1.554016083 Solving 0.7142857145 + p = 1.554016083 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + p = 1.554016083 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + p = 1.554016083 + -0.7142857145 p = 1.554016083 + -0.7142857145 Combine like terms: 1.554016083 + -0.7142857145 = 0.8397303685 p = 0.8397303685 Simplifying p = 0.8397303685

Subproblem 2

p + 0.7142857145 = -1.554016083 Simplifying p + 0.7142857145 = -1.554016083 Reorder the terms: 0.7142857145 + p = -1.554016083 Solving 0.7142857145 + p = -1.554016083 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + p = -1.554016083 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + p = -1.554016083 + -0.7142857145 p = -1.554016083 + -0.7142857145 Combine like terms: -1.554016083 + -0.7142857145 = -2.2683017975 p = -2.2683017975 Simplifying p = -2.2683017975

Solution

The solution to the problem is based on the solutions from the subproblems. p = {0.8397303685, -2.2683017975}

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