3b^2+2b-12=0

Simple and best practice solution for 3b^2+2b-12=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+2b-12=0 equation:


Simplifying
3b2 + 2b + -12 = 0

Reorder the terms:
-12 + 2b + 3b2 = 0

Solving
-12 + 2b + 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'.
-4 + 0.6666666667b + b2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 0.6666666667b + 4 + b2 = 0 + 4

Reorder the terms:
-4 + 4 + 0.6666666667b + b2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 0.6666666667b + b2 = 0 + 4
0.6666666667b + b2 = 0 + 4

Combine like terms: 0 + 4 = 4
0.6666666667b + b2 = 4

The b term is 0.6666666667b.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667b + 0.1111111112 + b2 = 4 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667b + b2 = 4 + 0.1111111112

Combine like terms: 4 + 0.1111111112 = 4.1111111112
0.1111111112 + 0.6666666667b + b2 = 4.1111111112

Factor a perfect square on the left side:
(b + 0.3333333334)(b + 0.3333333334) = 4.1111111112

Calculate the square root of the right side: 2.02758751

Break this problem into two subproblems by setting 
(b + 0.3333333334) equal to 2.02758751 and -2.02758751.

Subproblem 1

b + 0.3333333334 = 2.02758751 Simplifying b + 0.3333333334 = 2.02758751 Reorder the terms: 0.3333333334 + b = 2.02758751 Solving 0.3333333334 + b = 2.02758751 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + b = 2.02758751 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + b = 2.02758751 + -0.3333333334 b = 2.02758751 + -0.3333333334 Combine like terms: 2.02758751 + -0.3333333334 = 1.6942541766 b = 1.6942541766 Simplifying b = 1.6942541766

Subproblem 2

b + 0.3333333334 = -2.02758751 Simplifying b + 0.3333333334 = -2.02758751 Reorder the terms: 0.3333333334 + b = -2.02758751 Solving 0.3333333334 + b = -2.02758751 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + b = -2.02758751 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + b = -2.02758751 + -0.3333333334 b = -2.02758751 + -0.3333333334 Combine like terms: -2.02758751 + -0.3333333334 = -2.3609208434 b = -2.3609208434 Simplifying b = -2.3609208434

Solution

The solution to the problem is based on the solutions from the subproblems. b = {1.6942541766, -2.3609208434}

See similar equations:

| 1/2=f/8+1/4 | | 2=-5(4x+3)+21x | | 9p^2+18p-99=-9 | | -5/8-(-2/7)= | | x^2+15=-56 | | 8n^2+16n-94=4 | | abs(4x+5)=abs(4x+7) | | (3x^2-5x+1)-(x^2-7x+5)= | | 16z^6-576z^4=0 | | 5x^2-12x-11=0 | | x^3-2x-75=0 | | K^2+12k-3=10 | | -a-2x/5a+7a-7x/5a | | 18=20+a/35 | | x-30.001=-3 | | (3y/2x^5y^2)/(9y/10x) | | x(5x+26)+33=0 | | 98x^2=50 | | 1/5x-4=0 | | 1/5x+4 | | m+1+5+4=m+m+4 | | 8n^2-24=0 | | -4x+7=-6+2x | | 3t^(1/2)-4=0 | | -6+2x-1=22+2x | | 7+2r=5 | | (w^3-4w^2+7w-12)/(w-3) | | (x-2)(x+5)=9x-10 | | x^3-3x^2+7x+(-21)=0 | | 3x+4x+30=85+x+2x | | x^3-3x^2+7x-21=0 | | 6/(3w+9)+4/(2w+6)=0 |

Equations solver categories