v^2+17v+10=

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Solution for v^2+17v+10= equation:


Simplifying
v2 + 17v + 10 = 0

Reorder the terms:
10 + 17v + v2 = 0

Solving
10 + 17v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 17v + -10 + v2 = 0 + -10

Reorder the terms:
10 + -10 + 17v + v2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 17v + v2 = 0 + -10
17v + v2 = 0 + -10

Combine like terms: 0 + -10 = -10
17v + v2 = -10

The v term is 17v.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17v + 72.25 + v2 = -10 + 72.25

Reorder the terms:
72.25 + 17v + v2 = -10 + 72.25

Combine like terms: -10 + 72.25 = 62.25
72.25 + 17v + v2 = 62.25

Factor a perfect square on the left side:
(v + 8.5)(v + 8.5) = 62.25

Calculate the square root of the right side: 7.889866919

Break this problem into two subproblems by setting 
(v + 8.5) equal to 7.889866919 and -7.889866919.

Subproblem 1

v + 8.5 = 7.889866919 Simplifying v + 8.5 = 7.889866919 Reorder the terms: 8.5 + v = 7.889866919 Solving 8.5 + v = 7.889866919 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + v = 7.889866919 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + v = 7.889866919 + -8.5 v = 7.889866919 + -8.5 Combine like terms: 7.889866919 + -8.5 = -0.610133081 v = -0.610133081 Simplifying v = -0.610133081

Subproblem 2

v + 8.5 = -7.889866919 Simplifying v + 8.5 = -7.889866919 Reorder the terms: 8.5 + v = -7.889866919 Solving 8.5 + v = -7.889866919 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + v = -7.889866919 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + v = -7.889866919 + -8.5 v = -7.889866919 + -8.5 Combine like terms: -7.889866919 + -8.5 = -16.389866919 v = -16.389866919 Simplifying v = -16.389866919

Solution

The solution to the problem is based on the solutions from the subproblems. v = {-0.610133081, -16.389866919}

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