v^2+22v-57=0

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Solution for v^2+22v-57=0 equation:


Simplifying
v2 + 22v + -57 = 0

Reorder the terms:
-57 + 22v + v2 = 0

Solving
-57 + 22v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '57' to each side of the equation.
-57 + 22v + 57 + v2 = 0 + 57

Reorder the terms:
-57 + 57 + 22v + v2 = 0 + 57

Combine like terms: -57 + 57 = 0
0 + 22v + v2 = 0 + 57
22v + v2 = 0 + 57

Combine like terms: 0 + 57 = 57
22v + v2 = 57

The v term is 22v.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22v + 121 + v2 = 57 + 121

Reorder the terms:
121 + 22v + v2 = 57 + 121

Combine like terms: 57 + 121 = 178
121 + 22v + v2 = 178

Factor a perfect square on the left side:
(v + 11)(v + 11) = 178

Calculate the square root of the right side: 13.341664064

Break this problem into two subproblems by setting 
(v + 11) equal to 13.341664064 and -13.341664064.

Subproblem 1

v + 11 = 13.341664064 Simplifying v + 11 = 13.341664064 Reorder the terms: 11 + v = 13.341664064 Solving 11 + v = 13.341664064 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + v = 13.341664064 + -11 Combine like terms: 11 + -11 = 0 0 + v = 13.341664064 + -11 v = 13.341664064 + -11 Combine like terms: 13.341664064 + -11 = 2.341664064 v = 2.341664064 Simplifying v = 2.341664064

Subproblem 2

v + 11 = -13.341664064 Simplifying v + 11 = -13.341664064 Reorder the terms: 11 + v = -13.341664064 Solving 11 + v = -13.341664064 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + v = -13.341664064 + -11 Combine like terms: 11 + -11 = 0 0 + v = -13.341664064 + -11 v = -13.341664064 + -11 Combine like terms: -13.341664064 + -11 = -24.341664064 v = -24.341664064 Simplifying v = -24.341664064

Solution

The solution to the problem is based on the solutions from the subproblems. v = {2.341664064, -24.341664064}

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