8p^2-3p-10=20

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Solution for 8p^2-3p-10=20 equation:


Simplifying
8p2 + -3p + -10 = 20

Reorder the terms:
-10 + -3p + 8p2 = 20

Solving
-10 + -3p + 8p2 = 20

Solving for variable 'p'.

Reorder the terms:
-10 + -20 + -3p + 8p2 = 20 + -20

Combine like terms: -10 + -20 = -30
-30 + -3p + 8p2 = 20 + -20

Combine like terms: 20 + -20 = 0
-30 + -3p + 8p2 = 0

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

Divide each side by '8'.
-3.75 + -0.375p + p2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + -0.375p + 3.75 + p2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + -0.375p + p2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + -0.375p + p2 = 0 + 3.75
-0.375p + p2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
-0.375p + p2 = 3.75

The p term is -0.375p.  Take half its coefficient (-0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
-0.375p + 0.03515625 + p2 = 3.75 + 0.03515625

Reorder the terms:
0.03515625 + -0.375p + p2 = 3.75 + 0.03515625

Combine like terms: 3.75 + 0.03515625 = 3.78515625
0.03515625 + -0.375p + p2 = 3.78515625

Factor a perfect square on the left side:
(p + -0.1875)(p + -0.1875) = 3.78515625

Calculate the square root of the right side: 1.945547802

Break this problem into two subproblems by setting 
(p + -0.1875) equal to 1.945547802 and -1.945547802.

Subproblem 1

p + -0.1875 = 1.945547802 Simplifying p + -0.1875 = 1.945547802 Reorder the terms: -0.1875 + p = 1.945547802 Solving -0.1875 + p = 1.945547802 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + p = 1.945547802 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + p = 1.945547802 + 0.1875 p = 1.945547802 + 0.1875 Combine like terms: 1.945547802 + 0.1875 = 2.133047802 p = 2.133047802 Simplifying p = 2.133047802

Subproblem 2

p + -0.1875 = -1.945547802 Simplifying p + -0.1875 = -1.945547802 Reorder the terms: -0.1875 + p = -1.945547802 Solving -0.1875 + p = -1.945547802 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + p = -1.945547802 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + p = -1.945547802 + 0.1875 p = -1.945547802 + 0.1875 Combine like terms: -1.945547802 + 0.1875 = -1.758047802 p = -1.758047802 Simplifying p = -1.758047802

Solution

The solution to the problem is based on the solutions from the subproblems. p = {2.133047802, -1.758047802}

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