-2q^2-58q-70=0

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Solution for -2q^2-58q-70=0 equation: 


Simplifying
-2q2 + -58q + -70 = 0

Reorder the terms:
-70 + -58q + -2q2 = 0

Solving
-70 + -58q + -2q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(35 + 29q + q2) = 0

Ignore the factor -2.

Subproblem 1
Set the factor '(35 + 29q + q2)' equal to zero and attempt to solve:

Simplifying
35 + 29q + q2 = 0

Solving
35 + 29q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + 29q + -35 + q2 = 0 + -35

Reorder the terms:
35 + -35 + 29q + q2 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + 29q + q2 = 0 + -35
29q + q2 = 0 + -35

Combine like terms: 0 + -35 = -35
29q + q2 = -35

The q term is 29q.  Take half its coefficient (14.5).
Square it (210.25) and add it to both sides.

Add '210.25' to each side of the equation.
29q + 210.25 + q2 = -35 + 210.25

Reorder the terms:
210.25 + 29q + q2 = -35 + 210.25

Combine like terms: -35 + 210.25 = 175.25
210.25 + 29q + q2 = 175.25

Factor a perfect square on the left side:
(q + 14.5)(q + 14.5) = 175.25

Calculate the square root of the right side: 13.238202295

Break this problem into two subproblems by setting 
(q + 14.5) equal to 13.238202295 and -13.238202295.


Subproblem 1
q + 14.5 = 13.238202295

Simplifying
q + 14.5 = 13.238202295

Reorder the terms:
14.5 + q = 13.238202295

Solving
14.5 + q = 13.238202295

Solving for variable 'q'.

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

Add '-14.5' to each side of the equation.
14.5 + -14.5 + q = 13.238202295 + -14.5

Combine like terms: 14.5 + -14.5 = 0.0
0.0 + q = 13.238202295 + -14.5
q = 13.238202295 + -14.5

Combine like terms: 13.238202295 + -14.5 = -1.261797705
q = -1.261797705

Simplifying
q = -1.261797705


Subproblem 2
q + 14.5 = -13.238202295

Simplifying
q + 14.5 = -13.238202295

Reorder the terms:
14.5 + q = -13.238202295

Solving
14.5 + q = -13.238202295

Solving for variable 'q'.

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

Add '-14.5' to each side of the equation.
14.5 + -14.5 + q = -13.238202295 + -14.5

Combine like terms: 14.5 + -14.5 = 0.0
0.0 + q = -13.238202295 + -14.5
q = -13.238202295 + -14.5

Combine like terms: -13.238202295 + -14.5 = -27.738202295
q = -27.738202295

Simplifying
q = -27.738202295


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {-1.261797705, -27.738202295}
Solution
q = {-1.261797705, -27.738202295}

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