6.25p^2-8.99p=8.05

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Solution for 6.25p^2-8.99p=8.05 equation:


Simplifying
6.25p2 + -8.99p = 8.05

Reorder the terms:
-8.99p + 6.25p2 = 8.05

Solving
-8.99p + 6.25p2 = 8.05

Solving for variable 'p'.

Reorder the terms:
-8.05 + -8.99p + 6.25p2 = 8.05 + -8.05

Combine like terms: 8.05 + -8.05 = 0.00
-8.05 + -8.99p + 6.25p2 = 0.00

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

Divide each side by '6.25'.
-1.288 + -1.4384p + p2 = 0

Move the constant term to the right:

Add '1.288' to each side of the equation.
-1.288 + -1.4384p + 1.288 + p2 = 0 + 1.288

Reorder the terms:
-1.288 + 1.288 + -1.4384p + p2 = 0 + 1.288

Combine like terms: -1.288 + 1.288 = 0.000
0.000 + -1.4384p + p2 = 0 + 1.288
-1.4384p + p2 = 0 + 1.288

Combine like terms: 0 + 1.288 = 1.288
-1.4384p + p2 = 1.288

The p term is -1.4384p.  Take half its coefficient (-0.7192).
Square it (0.51724864) and add it to both sides.

Add '0.51724864' to each side of the equation.
-1.4384p + 0.51724864 + p2 = 1.288 + 0.51724864

Reorder the terms:
0.51724864 + -1.4384p + p2 = 1.288 + 0.51724864

Combine like terms: 1.288 + 0.51724864 = 1.80524864
0.51724864 + -1.4384p + p2 = 1.80524864

Factor a perfect square on the left side:
(p + -0.7192)(p + -0.7192) = 1.80524864

Calculate the square root of the right side: 1.343595415

Break this problem into two subproblems by setting 
(p + -0.7192) equal to 1.343595415 and -1.343595415.

Subproblem 1

p + -0.7192 = 1.343595415 Simplifying p + -0.7192 = 1.343595415 Reorder the terms: -0.7192 + p = 1.343595415 Solving -0.7192 + p = 1.343595415 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.7192' to each side of the equation. -0.7192 + 0.7192 + p = 1.343595415 + 0.7192 Combine like terms: -0.7192 + 0.7192 = 0.0000 0.0000 + p = 1.343595415 + 0.7192 p = 1.343595415 + 0.7192 Combine like terms: 1.343595415 + 0.7192 = 2.062795415 p = 2.062795415 Simplifying p = 2.062795415

Subproblem 2

p + -0.7192 = -1.343595415 Simplifying p + -0.7192 = -1.343595415 Reorder the terms: -0.7192 + p = -1.343595415 Solving -0.7192 + p = -1.343595415 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.7192' to each side of the equation. -0.7192 + 0.7192 + p = -1.343595415 + 0.7192 Combine like terms: -0.7192 + 0.7192 = 0.0000 0.0000 + p = -1.343595415 + 0.7192 p = -1.343595415 + 0.7192 Combine like terms: -1.343595415 + 0.7192 = -0.624395415 p = -0.624395415 Simplifying p = -0.624395415

Solution

The solution to the problem is based on the solutions from the subproblems. p = {2.062795415, -0.624395415}

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