v^2-6v-79=6

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Solution for v^2-6v-79=6 equation:


Simplifying
v2 + -6v + -79 = 6

Reorder the terms:
-79 + -6v + v2 = 6

Solving
-79 + -6v + v2 = 6

Solving for variable 'v'.

Reorder the terms:
-79 + -6 + -6v + v2 = 6 + -6

Combine like terms: -79 + -6 = -85
-85 + -6v + v2 = 6 + -6

Combine like terms: 6 + -6 = 0
-85 + -6v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '85' to each side of the equation.
-85 + -6v + 85 + v2 = 0 + 85

Reorder the terms:
-85 + 85 + -6v + v2 = 0 + 85

Combine like terms: -85 + 85 = 0
0 + -6v + v2 = 0 + 85
-6v + v2 = 0 + 85

Combine like terms: 0 + 85 = 85
-6v + v2 = 85

The v term is -6v.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6v + 9 + v2 = 85 + 9

Reorder the terms:
9 + -6v + v2 = 85 + 9

Combine like terms: 85 + 9 = 94
9 + -6v + v2 = 94

Factor a perfect square on the left side:
(v + -3)(v + -3) = 94

Calculate the square root of the right side: 9.695359715

Break this problem into two subproblems by setting 
(v + -3) equal to 9.695359715 and -9.695359715.

Subproblem 1

v + -3 = 9.695359715 Simplifying v + -3 = 9.695359715 Reorder the terms: -3 + v = 9.695359715 Solving -3 + v = 9.695359715 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + v = 9.695359715 + 3 Combine like terms: -3 + 3 = 0 0 + v = 9.695359715 + 3 v = 9.695359715 + 3 Combine like terms: 9.695359715 + 3 = 12.695359715 v = 12.695359715 Simplifying v = 12.695359715

Subproblem 2

v + -3 = -9.695359715 Simplifying v + -3 = -9.695359715 Reorder the terms: -3 + v = -9.695359715 Solving -3 + v = -9.695359715 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + v = -9.695359715 + 3 Combine like terms: -3 + 3 = 0 0 + v = -9.695359715 + 3 v = -9.695359715 + 3 Combine like terms: -9.695359715 + 3 = -6.695359715 v = -6.695359715 Simplifying v = -6.695359715

Solution

The solution to the problem is based on the solutions from the subproblems. v = {12.695359715, -6.695359715}

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