10p^2+27p-18=

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Solution for 10p^2+27p-18= equation:


Simplifying
10p2 + 27p + -18 = 0

Reorder the terms:
-18 + 27p + 10p2 = 0

Solving
-18 + 27p + 10p2 = 0

Solving for variable 'p'.

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

Divide each side by '10'.
-1.8 + 2.7p + p2 = 0

Move the constant term to the right:

Add '1.8' to each side of the equation.
-1.8 + 2.7p + 1.8 + p2 = 0 + 1.8

Reorder the terms:
-1.8 + 1.8 + 2.7p + p2 = 0 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + 2.7p + p2 = 0 + 1.8
2.7p + p2 = 0 + 1.8

Combine like terms: 0 + 1.8 = 1.8
2.7p + p2 = 1.8

The p term is 2.7p.  Take half its coefficient (1.35).
Square it (1.8225) and add it to both sides.

Add '1.8225' to each side of the equation.
2.7p + 1.8225 + p2 = 1.8 + 1.8225

Reorder the terms:
1.8225 + 2.7p + p2 = 1.8 + 1.8225

Combine like terms: 1.8 + 1.8225 = 3.6225
1.8225 + 2.7p + p2 = 3.6225

Factor a perfect square on the left side:
(p + 1.35)(p + 1.35) = 3.6225

Calculate the square root of the right side: 1.903286631

Break this problem into two subproblems by setting 
(p + 1.35) equal to 1.903286631 and -1.903286631.

Subproblem 1

p + 1.35 = 1.903286631 Simplifying p + 1.35 = 1.903286631 Reorder the terms: 1.35 + p = 1.903286631 Solving 1.35 + p = 1.903286631 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.35' to each side of the equation. 1.35 + -1.35 + p = 1.903286631 + -1.35 Combine like terms: 1.35 + -1.35 = 0.00 0.00 + p = 1.903286631 + -1.35 p = 1.903286631 + -1.35 Combine like terms: 1.903286631 + -1.35 = 0.553286631 p = 0.553286631 Simplifying p = 0.553286631

Subproblem 2

p + 1.35 = -1.903286631 Simplifying p + 1.35 = -1.903286631 Reorder the terms: 1.35 + p = -1.903286631 Solving 1.35 + p = -1.903286631 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.35' to each side of the equation. 1.35 + -1.35 + p = -1.903286631 + -1.35 Combine like terms: 1.35 + -1.35 = 0.00 0.00 + p = -1.903286631 + -1.35 p = -1.903286631 + -1.35 Combine like terms: -1.903286631 + -1.35 = -3.253286631 p = -3.253286631 Simplifying p = -3.253286631

Solution

The solution to the problem is based on the solutions from the subproblems. p = {0.553286631, -3.253286631}

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