v^2=8v-7

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Solution for v^2=8v-7 equation:


Simplifying
v2 = 8v + -7

Reorder the terms:
v2 = -7 + 8v

Solving
v2 = -7 + 8v

Solving for variable 'v'.

Reorder the terms:
7 + -8v + v2 = -7 + 8v + 7 + -8v

Reorder the terms:
7 + -8v + v2 = -7 + 7 + 8v + -8v

Combine like terms: -7 + 7 = 0
7 + -8v + v2 = 0 + 8v + -8v
7 + -8v + v2 = 8v + -8v

Combine like terms: 8v + -8v = 0
7 + -8v + v2 = 0

Factor a trinomial.
(1 + -1v)(7 + -1v) = 0

Subproblem 1

Set the factor '(1 + -1v)' equal to zero and attempt to solve: Simplifying 1 + -1v = 0 Solving 1 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1v = 0 + -1 -1v = 0 + -1 Combine like terms: 0 + -1 = -1 -1v = -1 Divide each side by '-1'. v = 1 Simplifying v = 1

Subproblem 2

Set the factor '(7 + -1v)' equal to zero and attempt to solve: Simplifying 7 + -1v = 0 Solving 7 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1v = 0 + -7 -1v = 0 + -7 Combine like terms: 0 + -7 = -7 -1v = -7 Divide each side by '-1'. v = 7 Simplifying v = 7

Solution

v = {1, 7}

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