v^2+6v-45=0

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Solution for v^2+6v-45=0 equation:


Simplifying
v2 + 6v + -45 = 0

Reorder the terms:
-45 + 6v + v2 = 0

Solving
-45 + 6v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 6v + 45 + v2 = 0 + 45

Reorder the terms:
-45 + 45 + 6v + v2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 6v + v2 = 0 + 45
6v + v2 = 0 + 45

Combine like terms: 0 + 45 = 45
6v + v2 = 45

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 = 45 + 9

Reorder the terms:
9 + 6v + v2 = 45 + 9

Combine like terms: 45 + 9 = 54
9 + 6v + v2 = 54

Factor a perfect square on the left side:
(v + 3)(v + 3) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(v + 3) equal to 7.348469228 and -7.348469228.

Subproblem 1

v + 3 = 7.348469228 Simplifying v + 3 = 7.348469228 Reorder the terms: 3 + v = 7.348469228 Solving 3 + v = 7.348469228 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 = 7.348469228 + -3 Combine like terms: 3 + -3 = 0 0 + v = 7.348469228 + -3 v = 7.348469228 + -3 Combine like terms: 7.348469228 + -3 = 4.348469228 v = 4.348469228 Simplifying v = 4.348469228

Subproblem 2

v + 3 = -7.348469228 Simplifying v + 3 = -7.348469228 Reorder the terms: 3 + v = -7.348469228 Solving 3 + v = -7.348469228 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 = -7.348469228 + -3 Combine like terms: 3 + -3 = 0 0 + v = -7.348469228 + -3 v = -7.348469228 + -3 Combine like terms: -7.348469228 + -3 = -10.348469228 v = -10.348469228 Simplifying v = -10.348469228

Solution

The solution to the problem is based on the solutions from the subproblems. v = {4.348469228, -10.348469228}

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