v^2-8v-7=0

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Solution for v^2-8v-7=0 equation:


Simplifying
v2 + -8v + -7 = 0

Reorder the terms:
-7 + -8v + v2 = 0

Solving
-7 + -8v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -8v + 7 + v2 = 0 + 7

Reorder the terms:
-7 + 7 + -8v + v2 = 0 + 7

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

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

The v term is -8v.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8v + 16 + v2 = 7 + 16

Reorder the terms:
16 + -8v + v2 = 7 + 16

Combine like terms: 7 + 16 = 23
16 + -8v + v2 = 23

Factor a perfect square on the left side:
(v + -4)(v + -4) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(v + -4) equal to 4.795831523 and -4.795831523.


Subproblem 1
v + -4 = 4.795831523

Simplifying
v + -4 = 4.795831523

Reorder the terms:
-4 + v = 4.795831523

Solving
-4 + v = 4.795831523

Solving for variable 'v'.

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

Add '4' to each side of the equation.
-4 + 4 + v = 4.795831523 + 4

Combine like terms: -4 + 4 = 0
0 + v = 4.795831523 + 4
v = 4.795831523 + 4

Combine like terms: 4.795831523 + 4 = 8.795831523
v = 8.795831523

Simplifying
v = 8.795831523


Subproblem 2
v + -4 = -4.795831523

Simplifying
v + -4 = -4.795831523

Reorder the terms:
-4 + v = -4.795831523

Solving
-4 + v = -4.795831523

Solving for variable 'v'.

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

Add '4' to each side of the equation.
-4 + 4 + v = -4.795831523 + 4

Combine like terms: -4 + 4 = 0
0 + v = -4.795831523 + 4
v = -4.795831523 + 4

Combine like terms: -4.795831523 + 4 = -0.795831523
v = -0.795831523

Simplifying
v = -0.795831523


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {8.795831523, -0.795831523}

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