3n^2-17n-70=0

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Solution for 3n^2-17n-70=0 equation: 


Simplifying
3n2 + -17n + -70 = 0

Reorder the terms:
-70 + -17n + 3n2 = 0

Solving
-70 + -17n + 3n2 = 0

Solving for variable 'n'.

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

Divide each side by '3'.
-23.33333333 + -5.666666667n + n2 = 0

Move the constant term to the right:

Add '23.33333333' to each side of the equation.
-23.33333333 + -5.666666667n + 23.33333333 + n2 = 0 + 23.33333333

Reorder the terms:
-23.33333333 + 23.33333333 + -5.666666667n + n2 = 0 + 23.33333333

Combine like terms: -23.33333333 + 23.33333333 = 0.00000000
0.00000000 + -5.666666667n + n2 = 0 + 23.33333333
-5.666666667n + n2 = 0 + 23.33333333

Combine like terms: 0 + 23.33333333 = 23.33333333
-5.666666667n + n2 = 23.33333333

The n term is -5.666666667n.  Take half its coefficient (-2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
-5.666666667n + 8.027777782 + n2 = 23.33333333 + 8.027777782

Reorder the terms:
8.027777782 + -5.666666667n + n2 = 23.33333333 + 8.027777782

Combine like terms: 23.33333333 + 8.027777782 = 31.361111112
8.027777782 + -5.666666667n + n2 = 31.361111112

Factor a perfect square on the left side:
(n + -2.833333334)(n + -2.833333334) = 31.361111112

Calculate the square root of the right side: 5.600099206

Break this problem into two subproblems by setting 
(n + -2.833333334) equal to 5.600099206 and -5.600099206.


Subproblem 1
n + -2.833333334 = 5.600099206

Simplifying
n + -2.833333334 = 5.600099206

Reorder the terms:
-2.833333334 + n = 5.600099206

Solving
-2.833333334 + n = 5.600099206

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + n = 5.600099206 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + n = 5.600099206 + 2.833333334
n = 5.600099206 + 2.833333334

Combine like terms: 5.600099206 + 2.833333334 = 8.43343254
n = 8.43343254

Simplifying
n = 8.43343254


Subproblem 2
n + -2.833333334 = -5.600099206

Simplifying
n + -2.833333334 = -5.600099206

Reorder the terms:
-2.833333334 + n = -5.600099206

Solving
-2.833333334 + n = -5.600099206

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + n = -5.600099206 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + n = -5.600099206 + 2.833333334
n = -5.600099206 + 2.833333334

Combine like terms: -5.600099206 + 2.833333334 = -2.766765872
n = -2.766765872

Simplifying
n = -2.766765872


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {8.43343254, -2.766765872}

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