3b^2-12b+7=0

Simple and best practice solution for 3b^2-12b+7=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^2-12b+7=0 equation:


Simplifying
3b2 + -12b + 7 = 0

Reorder the terms:
7 + -12b + 3b2 = 0

Solving
7 + -12b + 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'.
2.333333333 + -4b + b2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -4b + -2.333333333 + b2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -4b + b2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -4b + b2 = 0 + -2.333333333
-4b + b2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-4b + b2 = -2.333333333

The b term is -4b.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4b + 4 + b2 = -2.333333333 + 4

Reorder the terms:
4 + -4b + b2 = -2.333333333 + 4

Combine like terms: -2.333333333 + 4 = 1.666666667
4 + -4b + b2 = 1.666666667

Factor a perfect square on the left side:
(b + -2)(b + -2) = 1.666666667

Calculate the square root of the right side: 1.290994449

Break this problem into two subproblems by setting 
(b + -2) equal to 1.290994449 and -1.290994449.


Subproblem 1
b + -2 = 1.290994449

Simplifying
b + -2 = 1.290994449

Reorder the terms:
-2 + b = 1.290994449

Solving
-2 + b = 1.290994449

Solving for variable 'b'.

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

Add '2' to each side of the equation.
-2 + 2 + b = 1.290994449 + 2

Combine like terms: -2 + 2 = 0
0 + b = 1.290994449 + 2
b = 1.290994449 + 2

Combine like terms: 1.290994449 + 2 = 3.290994449
b = 3.290994449

Simplifying
b = 3.290994449


Subproblem 2
b + -2 = -1.290994449

Simplifying
b + -2 = -1.290994449

Reorder the terms:
-2 + b = -1.290994449

Solving
-2 + b = -1.290994449

Solving for variable 'b'.

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

Add '2' to each side of the equation.
-2 + 2 + b = -1.290994449 + 2

Combine like terms: -2 + 2 = 0
0 + b = -1.290994449 + 2
b = -1.290994449 + 2

Combine like terms: -1.290994449 + 2 = 0.709005551
b = 0.709005551

Simplifying
b = 0.709005551


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {3.290994449, 0.709005551}

See similar equations:

| 32+94=54 | | X^2+27x+170=0 | | x-3y+36=0 | | (123+57*2)+6x-21=360 | | 20x^2+62x+30=0 | | 5x^2-60x+100=0 | | 2(3x-11)=17-7x | | -3+x=3 | | y=3(-2) | | 24.6+3a=9.54 | | Y+10=-5 | | a=(25+0.75h)-5 | | X^2+11x=33.75 | | 5n+4=(n+1)-2n | | 14x-28=28x+70 | | 9=4k-7k | | 2-y=9 | | -14x=-322 | | -h+6=-(h-5) | | 5.8+4.5/(-1.5)= | | Y=y-9 | | 5.8+4.5/-1.5= | | 19b+14=65 | | 1600=x+x*.08 | | 5x-15=4x+13 | | 0-y=9 | | (52+128+52+28)+4x=360 | | -1(x-2)= | | 2x-2=x+54 | | 10t+20-13t-9= | | 2x-17+3x+2+2x+19+83=360 | | (x+5)+(3x+5)=45 |

Equations solver categories