2v^2-22v+61=(v-7)(v-7)

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Solution for 2v^2-22v+61=(v-7)(v-7) equation: 


Simplifying
2v2 + -22v + 61 = (v + -7)(v + -7)

Reorder the terms:
61 + -22v + 2v2 = (v + -7)(v + -7)

Reorder the terms:
61 + -22v + 2v2 = (-7 + v)(v + -7)

Reorder the terms:
61 + -22v + 2v2 = (-7 + v)(-7 + v)

Multiply (-7 + v) * (-7 + v)
61 + -22v + 2v2 = (-7(-7 + v) + v(-7 + v))
61 + -22v + 2v2 = ((-7 * -7 + v * -7) + v(-7 + v))
61 + -22v + 2v2 = ((49 + -7v) + v(-7 + v))
61 + -22v + 2v2 = (49 + -7v + (-7 * v + v * v))
61 + -22v + 2v2 = (49 + -7v + (-7v + v2))

Combine like terms: -7v + -7v = -14v
61 + -22v + 2v2 = (49 + -14v + v2)

Solving
61 + -22v + 2v2 = 49 + -14v + v2

Solving for variable 'v'.

Reorder the terms:
61 + -49 + -22v + 14v + 2v2 + -1v2 = 49 + -14v + v2 + -49 + 14v + -1v2

Combine like terms: 61 + -49 = 12
12 + -22v + 14v + 2v2 + -1v2 = 49 + -14v + v2 + -49 + 14v + -1v2

Combine like terms: -22v + 14v = -8v
12 + -8v + 2v2 + -1v2 = 49 + -14v + v2 + -49 + 14v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
12 + -8v + 1v2 = 49 + -14v + v2 + -49 + 14v + -1v2

Reorder the terms:
12 + -8v + 1v2 = 49 + -49 + -14v + 14v + v2 + -1v2

Combine like terms: 49 + -49 = 0
12 + -8v + 1v2 = 0 + -14v + 14v + v2 + -1v2
12 + -8v + 1v2 = -14v + 14v + v2 + -1v2

Combine like terms: -14v + 14v = 0
12 + -8v + 1v2 = 0 + v2 + -1v2
12 + -8v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
12 + -8v + 1v2 = 0

Factor a trinomial.
(2 + -1v)(6 + -1v) = 0


Subproblem 1
Set the factor '(2 + -1v)' equal to zero and attempt to solve:

Simplifying
2 + -1v = 0

Solving
2 + -1v = 0

Move all terms containing v to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1v = 0 + -2
-1v = 0 + -2

Combine like terms: 0 + -2 = -2
-1v = -2

Divide each side by '-1'.
v = 2

Simplifying
v = 2

Subproblem 2
Set the factor '(6 + -1v)' equal to zero and attempt to solve:

Simplifying
6 + -1v = 0

Solving
6 + -1v = 0

Move all terms containing v to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1v = 0 + -6
-1v = 0 + -6

Combine like terms: 0 + -6 = -6
-1v = -6

Divide each side by '-1'.
v = 6

Simplifying
v = 6
Solution
v = {2, 6}

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