2p^2-10p+7=0

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Solution for 2p^2-10p+7=0 equation:


Simplifying
2p2 + -10p + 7 = 0

Reorder the terms:
7 + -10p + 2p2 = 0

Solving
7 + -10p + 2p2 = 0

Solving for variable 'p'.

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

Divide each side by '2'.
3.5 + -5p + p2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + -5p + -3.5 + p2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + -5p + p2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + -5p + p2 = 0 + -3.5
-5p + p2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
-5p + p2 = -3.5

The p term is -5p.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5p + 6.25 + p2 = -3.5 + 6.25

Reorder the terms:
6.25 + -5p + p2 = -3.5 + 6.25

Combine like terms: -3.5 + 6.25 = 2.75
6.25 + -5p + p2 = 2.75

Factor a perfect square on the left side:
(p + -2.5)(p + -2.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(p + -2.5) equal to 1.658312395 and -1.658312395.

Subproblem 1

p + -2.5 = 1.658312395 Simplifying p + -2.5 = 1.658312395 Reorder the terms: -2.5 + p = 1.658312395 Solving -2.5 + p = 1.658312395 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + p = 1.658312395 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + p = 1.658312395 + 2.5 p = 1.658312395 + 2.5 Combine like terms: 1.658312395 + 2.5 = 4.158312395 p = 4.158312395 Simplifying p = 4.158312395

Subproblem 2

p + -2.5 = -1.658312395 Simplifying p + -2.5 = -1.658312395 Reorder the terms: -2.5 + p = -1.658312395 Solving -2.5 + p = -1.658312395 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + p = -1.658312395 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + p = -1.658312395 + 2.5 p = -1.658312395 + 2.5 Combine like terms: -1.658312395 + 2.5 = 0.841687605 p = 0.841687605 Simplifying p = 0.841687605

Solution

The solution to the problem is based on the solutions from the subproblems. p = {4.158312395, 0.841687605}

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