5p^2+2=8p

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Solution for 5p^2+2=8p equation:


Simplifying
5p2 + 2 = 8p

Reorder the terms:
2 + 5p2 = 8p

Solving
2 + 5p2 = 8p

Solving for variable 'p'.

Reorder the terms:
2 + -8p + 5p2 = 8p + -8p

Combine like terms: 8p + -8p = 0
2 + -8p + 5p2 = 0

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

Divide each side by '5'.
0.4 + -1.6p + p2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + -1.6p + -0.4 + p2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + -1.6p + p2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + -1.6p + p2 = 0 + -0.4
-1.6p + p2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
-1.6p + p2 = -0.4

The p term is -1.6p.  Take half its coefficient (-0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
-1.6p + 0.64 + p2 = -0.4 + 0.64

Reorder the terms:
0.64 + -1.6p + p2 = -0.4 + 0.64

Combine like terms: -0.4 + 0.64 = 0.24
0.64 + -1.6p + p2 = 0.24

Factor a perfect square on the left side:
(p + -0.8)(p + -0.8) = 0.24

Calculate the square root of the right side: 0.489897949

Break this problem into two subproblems by setting 
(p + -0.8) equal to 0.489897949 and -0.489897949.

Subproblem 1

p + -0.8 = 0.489897949 Simplifying p + -0.8 = 0.489897949 Reorder the terms: -0.8 + p = 0.489897949 Solving -0.8 + p = 0.489897949 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + p = 0.489897949 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + p = 0.489897949 + 0.8 p = 0.489897949 + 0.8 Combine like terms: 0.489897949 + 0.8 = 1.289897949 p = 1.289897949 Simplifying p = 1.289897949

Subproblem 2

p + -0.8 = -0.489897949 Simplifying p + -0.8 = -0.489897949 Reorder the terms: -0.8 + p = -0.489897949 Solving -0.8 + p = -0.489897949 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + p = -0.489897949 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + p = -0.489897949 + 0.8 p = -0.489897949 + 0.8 Combine like terms: -0.489897949 + 0.8 = 0.310102051 p = 0.310102051 Simplifying p = 0.310102051

Solution

The solution to the problem is based on the solutions from the subproblems. p = {1.289897949, 0.310102051}

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