v^2-8v-3=3

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Solution for v^2-8v-3=3 equation:


Simplifying
v2 + -8v + -3 = 3

Reorder the terms:
-3 + -8v + v2 = 3

Solving
-3 + -8v + v2 = 3

Solving for variable 'v'.

Reorder the terms:
-3 + -3 + -8v + v2 = 3 + -3

Combine like terms: -3 + -3 = -6
-6 + -8v + v2 = 3 + -3

Combine like terms: 3 + -3 = 0
-6 + -8v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -8v + 6 + v2 = 0 + 6

Reorder the terms:
-6 + 6 + -8v + v2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -8v + v2 = 0 + 6
-8v + v2 = 0 + 6

Combine like terms: 0 + 6 = 6
-8v + v2 = 6

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 = 6 + 16

Reorder the terms:
16 + -8v + v2 = 6 + 16

Combine like terms: 6 + 16 = 22
16 + -8v + v2 = 22

Factor a perfect square on the left side:
(v + -4)(v + -4) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(v + -4) equal to 4.69041576 and -4.69041576.

Subproblem 1

v + -4 = 4.69041576 Simplifying v + -4 = 4.69041576 Reorder the terms: -4 + v = 4.69041576 Solving -4 + v = 4.69041576 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 = 4.69041576 + 4 Combine like terms: -4 + 4 = 0 0 + v = 4.69041576 + 4 v = 4.69041576 + 4 Combine like terms: 4.69041576 + 4 = 8.69041576 v = 8.69041576 Simplifying v = 8.69041576

Subproblem 2

v + -4 = -4.69041576 Simplifying v + -4 = -4.69041576 Reorder the terms: -4 + v = -4.69041576 Solving -4 + v = -4.69041576 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 = -4.69041576 + 4 Combine like terms: -4 + 4 = 0 0 + v = -4.69041576 + 4 v = -4.69041576 + 4 Combine like terms: -4.69041576 + 4 = -0.69041576 v = -0.69041576 Simplifying v = -0.69041576

Solution

The solution to the problem is based on the solutions from the subproblems. v = {8.69041576, -0.69041576}

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