2v^2+7v-34=-2

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Solution for 2v^2+7v-34=-2 equation:


Simplifying
2v2 + 7v + -34 = -2

Reorder the terms:
-34 + 7v + 2v2 = -2

Solving
-34 + 7v + 2v2 = -2

Solving for variable 'v'.

Reorder the terms:
-34 + 2 + 7v + 2v2 = -2 + 2

Combine like terms: -34 + 2 = -32
-32 + 7v + 2v2 = -2 + 2

Combine like terms: -2 + 2 = 0
-32 + 7v + 2v2 = 0

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

Divide each side by '2'.
-16 + 3.5v + v2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 3.5v + 16 + v2 = 0 + 16

Reorder the terms:
-16 + 16 + 3.5v + v2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 3.5v + v2 = 0 + 16
3.5v + v2 = 0 + 16

Combine like terms: 0 + 16 = 16
3.5v + v2 = 16

The v term is 3.5v.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5v + 3.0625 + v2 = 16 + 3.0625

Reorder the terms:
3.0625 + 3.5v + v2 = 16 + 3.0625

Combine like terms: 16 + 3.0625 = 19.0625
3.0625 + 3.5v + v2 = 19.0625

Factor a perfect square on the left side:
(v + 1.75)(v + 1.75) = 19.0625

Calculate the square root of the right side: 4.366062299

Break this problem into two subproblems by setting 
(v + 1.75) equal to 4.366062299 and -4.366062299.

Subproblem 1

v + 1.75 = 4.366062299 Simplifying v + 1.75 = 4.366062299 Reorder the terms: 1.75 + v = 4.366062299 Solving 1.75 + v = 4.366062299 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + v = 4.366062299 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + v = 4.366062299 + -1.75 v = 4.366062299 + -1.75 Combine like terms: 4.366062299 + -1.75 = 2.616062299 v = 2.616062299 Simplifying v = 2.616062299

Subproblem 2

v + 1.75 = -4.366062299 Simplifying v + 1.75 = -4.366062299 Reorder the terms: 1.75 + v = -4.366062299 Solving 1.75 + v = -4.366062299 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + v = -4.366062299 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + v = -4.366062299 + -1.75 v = -4.366062299 + -1.75 Combine like terms: -4.366062299 + -1.75 = -6.116062299 v = -6.116062299 Simplifying v = -6.116062299

Solution

The solution to the problem is based on the solutions from the subproblems. v = {2.616062299, -6.116062299}

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