3b^2-19b-6=0

Simple and best practice solution for 3b^2-19b-6=0 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 3b^2-19b-6=0 equation: 


Simplifying
3b2 + -19b + -6 = 0

Reorder the terms:
-6 + -19b + 3b2 = 0

Solving
-6 + -19b + 3b2 = 0

Solving for variable 'b'.

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

Divide each side by '3'.
-2 + -6.333333333b + b2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -6.333333333b + 2 + b2 = 0 + 2

Reorder the terms:
-2 + 2 + -6.333333333b + b2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -6.333333333b + b2 = 0 + 2
-6.333333333b + b2 = 0 + 2

Combine like terms: 0 + 2 = 2
-6.333333333b + b2 = 2

The b term is -6.333333333b.  Take half its coefficient (-3.166666667).
Square it (10.02777778) and add it to both sides.

Add '10.02777778' to each side of the equation.
-6.333333333b + 10.02777778 + b2 = 2 + 10.02777778

Reorder the terms:
10.02777778 + -6.333333333b + b2 = 2 + 10.02777778

Combine like terms: 2 + 10.02777778 = 12.02777778
10.02777778 + -6.333333333b + b2 = 12.02777778

Factor a perfect square on the left side:
(b + -3.166666667)(b + -3.166666667) = 12.02777778

Calculate the square root of the right side: 3.468108675

Break this problem into two subproblems by setting 
(b + -3.166666667) equal to 3.468108675 and -3.468108675.


Subproblem 1
b + -3.166666667 = 3.468108675

Simplifying
b + -3.166666667 = 3.468108675

Reorder the terms:
-3.166666667 + b = 3.468108675

Solving
-3.166666667 + b = 3.468108675

Solving for variable 'b'.

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

Add '3.166666667' to each side of the equation.
-3.166666667 + 3.166666667 + b = 3.468108675 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + b = 3.468108675 + 3.166666667
b = 3.468108675 + 3.166666667

Combine like terms: 3.468108675 + 3.166666667 = 6.634775342
b = 6.634775342

Simplifying
b = 6.634775342


Subproblem 2
b + -3.166666667 = -3.468108675

Simplifying
b + -3.166666667 = -3.468108675

Reorder the terms:
-3.166666667 + b = -3.468108675

Solving
-3.166666667 + b = -3.468108675

Solving for variable 'b'.

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

Add '3.166666667' to each side of the equation.
-3.166666667 + 3.166666667 + b = -3.468108675 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + b = -3.468108675 + 3.166666667
b = -3.468108675 + 3.166666667

Combine like terms: -3.468108675 + 3.166666667 = -0.301442008
b = -0.301442008

Simplifying
b = -0.301442008


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {6.634775342, -0.301442008}

See similar equations:

| 5y^2+7y=-2 | | -2(t+3)+8=24 | | 3x^2+9x-84=0 | | 0=9(k-2/3)+33 | | 2(5w)+2w=168 | | -6x-6=36 | | u^2+10u+21=0 | | 2a+3=.5(6+4a) | | w+5+2(w)=250 | | (x-5)(x+6)=0 | | 5a^2-3a+15=0 | | 4x^2-31x-90=0 | | 3x=7x-6 | | 24x-16=19x+29 | | -2.7=3.7 | | 4x+8=2(2x+4) | | 9x-1=8x+2 | | 4x+1=5x | | 3x-7-5x=5+x | | 2x^3+5y^3=0 | | .33(3x-6)=2x | | 5-4(2w-2)+w= | | 9x=-18(x+5) | | Y=2x^2-5x+15 | | 4x-6=7x-12 | | 6x-1=5x+1 | | 8x^6+999x^3=125 | | .5(x-4)=4x | | -12(x+6)=4(x-6) | | 5777=6677 | | 12(x-2)=-49(x+10) | | (x+2)(x-6)=20 |

Equations solver categories