v^2+6v-35=

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Solution for v^2+6v-35= equation:


Simplifying
v2 + 6v + -35 = 0

Reorder the terms:
-35 + 6v + v2 = 0

Solving
-35 + 6v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + 6v + 35 + v2 = 0 + 35

Reorder the terms:
-35 + 35 + 6v + v2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + 6v + v2 = 0 + 35
6v + v2 = 0 + 35

Combine like terms: 0 + 35 = 35
6v + v2 = 35

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 = 35 + 9

Reorder the terms:
9 + 6v + v2 = 35 + 9

Combine like terms: 35 + 9 = 44
9 + 6v + v2 = 44

Factor a perfect square on the left side:
(v + 3)(v + 3) = 44

Calculate the square root of the right side: 6.633249581

Break this problem into two subproblems by setting 
(v + 3) equal to 6.633249581 and -6.633249581.

Subproblem 1

v + 3 = 6.633249581 Simplifying v + 3 = 6.633249581 Reorder the terms: 3 + v = 6.633249581 Solving 3 + v = 6.633249581 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 = 6.633249581 + -3 Combine like terms: 3 + -3 = 0 0 + v = 6.633249581 + -3 v = 6.633249581 + -3 Combine like terms: 6.633249581 + -3 = 3.633249581 v = 3.633249581 Simplifying v = 3.633249581

Subproblem 2

v + 3 = -6.633249581 Simplifying v + 3 = -6.633249581 Reorder the terms: 3 + v = -6.633249581 Solving 3 + v = -6.633249581 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 = -6.633249581 + -3 Combine like terms: 3 + -3 = 0 0 + v = -6.633249581 + -3 v = -6.633249581 + -3 Combine like terms: -6.633249581 + -3 = -9.633249581 v = -9.633249581 Simplifying v = -9.633249581

Solution

The solution to the problem is based on the solutions from the subproblems. v = {3.633249581, -9.633249581}

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