-8v(1+6v)-7(v-5)=

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Solution for -8v(1+6v)-7(v-5)= equation: 


Simplifying
-8v(1 + 6v) + -7(v + -5) = 0
(1 * -8v + 6v * -8v) + -7(v + -5) = 0
(-8v + -48v2) + -7(v + -5) = 0

Reorder the terms:
-8v + -48v2 + -7(-5 + v) = 0
-8v + -48v2 + (-5 * -7 + v * -7) = 0
-8v + -48v2 + (35 + -7v) = 0

Reorder the terms:
35 + -8v + -7v + -48v2 = 0

Combine like terms: -8v + -7v = -15v
35 + -15v + -48v2 = 0

Solving
35 + -15v + -48v2 = 0

Solving for variable 'v'.

Begin completing the square.  Divide all terms by
-48 the coefficient of the squared term: 

Divide each side by '-48'.
-0.7291666667 + 0.3125v + v2 = 0

Move the constant term to the right:

Add '0.7291666667' to each side of the equation.
-0.7291666667 + 0.3125v + 0.7291666667 + v2 = 0 + 0.7291666667

Reorder the terms:
-0.7291666667 + 0.7291666667 + 0.3125v + v2 = 0 + 0.7291666667

Combine like terms: -0.7291666667 + 0.7291666667 = 0.0000000000
0.0000000000 + 0.3125v + v2 = 0 + 0.7291666667
0.3125v + v2 = 0 + 0.7291666667

Combine like terms: 0 + 0.7291666667 = 0.7291666667
0.3125v + v2 = 0.7291666667

The v term is 0.3125v.  Take half its coefficient (0.15625).
Square it (0.0244140625) and add it to both sides.

Add '0.0244140625' to each side of the equation.
0.3125v + 0.0244140625 + v2 = 0.7291666667 + 0.0244140625

Reorder the terms:
0.0244140625 + 0.3125v + v2 = 0.7291666667 + 0.0244140625

Combine like terms: 0.7291666667 + 0.0244140625 = 0.7535807292
0.0244140625 + 0.3125v + v2 = 0.7535807292

Factor a perfect square on the left side:
(v + 0.15625)(v + 0.15625) = 0.7535807292

Calculate the square root of the right side: 0.868090277

Break this problem into two subproblems by setting 
(v + 0.15625) equal to 0.868090277 and -0.868090277.


Subproblem 1
v + 0.15625 = 0.868090277

Simplifying
v + 0.15625 = 0.868090277

Reorder the terms:
0.15625 + v = 0.868090277

Solving
0.15625 + v = 0.868090277

Solving for variable 'v'.

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

Add '-0.15625' to each side of the equation.
0.15625 + -0.15625 + v = 0.868090277 + -0.15625

Combine like terms: 0.15625 + -0.15625 = 0.00000
0.00000 + v = 0.868090277 + -0.15625
v = 0.868090277 + -0.15625

Combine like terms: 0.868090277 + -0.15625 = 0.711840277
v = 0.711840277

Simplifying
v = 0.711840277


Subproblem 2
v + 0.15625 = -0.868090277

Simplifying
v + 0.15625 = -0.868090277

Reorder the terms:
0.15625 + v = -0.868090277

Solving
0.15625 + v = -0.868090277

Solving for variable 'v'.

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

Add '-0.15625' to each side of the equation.
0.15625 + -0.15625 + v = -0.868090277 + -0.15625

Combine like terms: 0.15625 + -0.15625 = 0.00000
0.00000 + v = -0.868090277 + -0.15625
v = -0.868090277 + -0.15625

Combine like terms: -0.868090277 + -0.15625 = -1.024340277
v = -1.024340277

Simplifying
v = -1.024340277


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {0.711840277, -1.024340277}

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