10p^2+4p+77=9

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Solution for 10p^2+4p+77=9 equation: 


Simplifying
10p2 + 4p + 77 = 9

Reorder the terms:
77 + 4p + 10p2 = 9

Solving
77 + 4p + 10p2 = 9

Solving for variable 'p'.

Reorder the terms:
77 + -9 + 4p + 10p2 = 9 + -9

Combine like terms: 77 + -9 = 68
68 + 4p + 10p2 = 9 + -9

Combine like terms: 9 + -9 = 0
68 + 4p + 10p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(34 + 2p + 5p2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(34 + 2p + 5p2)' equal to zero and attempt to solve:

Simplifying
34 + 2p + 5p2 = 0

Solving
34 + 2p + 5p2 = 0

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

Divide each side by '5'.
6.8 + 0.4p + p2 = 0

Move the constant term to the right:

Add '-6.8' to each side of the equation.
6.8 + 0.4p + -6.8 + p2 = 0 + -6.8

Reorder the terms:
6.8 + -6.8 + 0.4p + p2 = 0 + -6.8

Combine like terms: 6.8 + -6.8 = 0.0
0.0 + 0.4p + p2 = 0 + -6.8
0.4p + p2 = 0 + -6.8

Combine like terms: 0 + -6.8 = -6.8
0.4p + p2 = -6.8

The p term is 0.4p.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4p + 0.04 + p2 = -6.8 + 0.04

Reorder the terms:
0.04 + 0.4p + p2 = -6.8 + 0.04

Combine like terms: -6.8 + 0.04 = -6.76
0.04 + 0.4p + p2 = -6.76

Factor a perfect square on the left side:
(p + 0.2)(p + 0.2) = -6.76

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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