v^2-26v=31

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Solution for v^2-26v=31 equation:


Simplifying
v2 + -26v = 31

Reorder the terms:
-26v + v2 = 31

Solving
-26v + v2 = 31

Solving for variable 'v'.

Reorder the terms:
-31 + -26v + v2 = 31 + -31

Combine like terms: 31 + -31 = 0
-31 + -26v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + -26v + 31 + v2 = 0 + 31

Reorder the terms:
-31 + 31 + -26v + v2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -26v + v2 = 0 + 31
-26v + v2 = 0 + 31

Combine like terms: 0 + 31 = 31
-26v + v2 = 31

The v term is -26v.  Take half its coefficient (-13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
-26v + 169 + v2 = 31 + 169

Reorder the terms:
169 + -26v + v2 = 31 + 169

Combine like terms: 31 + 169 = 200
169 + -26v + v2 = 200

Factor a perfect square on the left side:
(v + -13)(v + -13) = 200

Calculate the square root of the right side: 14.142135624

Break this problem into two subproblems by setting 
(v + -13) equal to 14.142135624 and -14.142135624.

Subproblem 1

v + -13 = 14.142135624 Simplifying v + -13 = 14.142135624 Reorder the terms: -13 + v = 14.142135624 Solving -13 + v = 14.142135624 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + v = 14.142135624 + 13 Combine like terms: -13 + 13 = 0 0 + v = 14.142135624 + 13 v = 14.142135624 + 13 Combine like terms: 14.142135624 + 13 = 27.142135624 v = 27.142135624 Simplifying v = 27.142135624

Subproblem 2

v + -13 = -14.142135624 Simplifying v + -13 = -14.142135624 Reorder the terms: -13 + v = -14.142135624 Solving -13 + v = -14.142135624 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + v = -14.142135624 + 13 Combine like terms: -13 + 13 = 0 0 + v = -14.142135624 + 13 v = -14.142135624 + 13 Combine like terms: -14.142135624 + 13 = -1.142135624 v = -1.142135624 Simplifying v = -1.142135624

Solution

The solution to the problem is based on the solutions from the subproblems. v = {27.142135624, -1.142135624}

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