10.6=1.6+0.3v+0.003v^2

Simple and best practice solution for 10.6=1.6+0.3v+0.003v^2 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 10.6=1.6+0.3v+0.003v^2 equation:


Simplifying
10.6 = 1.6 + 0.3v + 0.003v2

Solving
10.6 = 1.6 + 0.3v + 0.003v2

Solving for variable 'v'.

Combine like terms: 10.6 + -1.6 = 9
9 + -0.3v + -0.003v2 = 1.6 + 0.3v + 0.003v2 + -1.6 + -0.3v + -0.003v2

Reorder the terms:
9 + -0.3v + -0.003v2 = 1.6 + -1.6 + 0.3v + -0.3v + 0.003v2 + -0.003v2

Combine like terms: 1.6 + -1.6 = 0.0
9 + -0.3v + -0.003v2 = 0.0 + 0.3v + -0.3v + 0.003v2 + -0.003v2
9 + -0.3v + -0.003v2 = 0.3v + -0.3v + 0.003v2 + -0.003v2

Combine like terms: 0.3v + -0.3v = 0.0
9 + -0.3v + -0.003v2 = 0.0 + 0.003v2 + -0.003v2
9 + -0.3v + -0.003v2 = 0.003v2 + -0.003v2

Combine like terms: 0.003v2 + -0.003v2 = 0.000
9 + -0.3v + -0.003v2 = 0.000

Begin completing the square.  Divide all terms by
-0.003 the coefficient of the squared term: 

Divide each side by '-0.003'.
-3000 + 100v + v2 = 0

Move the constant term to the right:

Add '3000' to each side of the equation.
-3000 + 100v + 3000 + v2 = 0 + 3000

Reorder the terms:
-3000 + 3000 + 100v + v2 = 0 + 3000

Combine like terms: -3000 + 3000 = 0
0 + 100v + v2 = 0 + 3000
100v + v2 = 0 + 3000

Combine like terms: 0 + 3000 = 3000
100v + v2 = 3000

The v term is 100v.  Take half its coefficient (50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
100v + 2500 + v2 = 3000 + 2500

Reorder the terms:
2500 + 100v + v2 = 3000 + 2500

Combine like terms: 3000 + 2500 = 5500
2500 + 100v + v2 = 5500

Factor a perfect square on the left side:
(v + 50)(v + 50) = 5500

Calculate the square root of the right side: 74.161984871

Break this problem into two subproblems by setting 
(v + 50) equal to 74.161984871 and -74.161984871.

Subproblem 1

v + 50 = 74.161984871 Simplifying v + 50 = 74.161984871 Reorder the terms: 50 + v = 74.161984871 Solving 50 + v = 74.161984871 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + v = 74.161984871 + -50 Combine like terms: 50 + -50 = 0 0 + v = 74.161984871 + -50 v = 74.161984871 + -50 Combine like terms: 74.161984871 + -50 = 24.161984871 v = 24.161984871 Simplifying v = 24.161984871

Subproblem 2

v + 50 = -74.161984871 Simplifying v + 50 = -74.161984871 Reorder the terms: 50 + v = -74.161984871 Solving 50 + v = -74.161984871 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + v = -74.161984871 + -50 Combine like terms: 50 + -50 = 0 0 + v = -74.161984871 + -50 v = -74.161984871 + -50 Combine like terms: -74.161984871 + -50 = -124.161984871 v = -124.161984871 Simplifying v = -124.161984871

Solution

The solution to the problem is based on the solutions from the subproblems. v = {24.161984871, -124.161984871}

See similar equations:

| 10.6=1.6+0.3v+0.003v | | 12x-12=9x+3 | | p-6=8-4p | | 3(4x-9)=81 | | 2x+14=42-2x | | 8-4k=-2 | | 10m= | | 76=70t-16t^2 | | 397+d=842 | | 4x+30=6x+13 | | 32-2x=7x+16 | | 14-8x=55-15x | | -48-8x=55-15x | | 3(2y+3)=5(2y+1) | | a+6=20 | | 10x^2+6x+29=0 | | 6x+5=3x+26 | | 94-6x=17x-4x | | 5y^4-7y^2+1=0 | | 5(x-2)=3(x+4) | | 2(d+3)=d+12 | | 4(2-x)+2(x+3)=15 | | 15x-3=3x+5 | | 2x-22=8-13x | | 6x+35=-1 | | B=8a+4x(a+3) | | 4(2-x)-2(x+3)=15 | | A=3x(a+5)+2a | | 7w+14=0 | | 5x+33=15x-57 | | 28x^2-25x=0 | | 4x^2+3x-1800=0 |

Equations solver categories