3q^2-16q+12=0

Simple and best practice solution for 3q^2-16q+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 3q^2-16q+12=0 equation:


Simplifying
3q2 + -16q + 12 = 0

Reorder the terms:
12 + -16q + 3q2 = 0

Solving
12 + -16q + 3q2 = 0

Solving for variable 'q'.

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

Divide each side by '3'.
4 + -5.333333333q + q2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -5.333333333q + -4 + q2 = 0 + -4

Reorder the terms:
4 + -4 + -5.333333333q + q2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5.333333333q + q2 = 0 + -4
-5.333333333q + q2 = 0 + -4

Combine like terms: 0 + -4 = -4
-5.333333333q + q2 = -4

The q term is -5.333333333q.  Take half its coefficient (-2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
-5.333333333q + 7.111111113 + q2 = -4 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333q + q2 = -4 + 7.111111113

Combine like terms: -4 + 7.111111113 = 3.111111113
7.111111113 + -5.333333333q + q2 = 3.111111113

Factor a perfect square on the left side:
(q + -2.666666667)(q + -2.666666667) = 3.111111113

Calculate the square root of the right side: 1.763834208

Break this problem into two subproblems by setting 
(q + -2.666666667) equal to 1.763834208 and -1.763834208.

Subproblem 1

q + -2.666666667 = 1.763834208 Simplifying q + -2.666666667 = 1.763834208 Reorder the terms: -2.666666667 + q = 1.763834208 Solving -2.666666667 + q = 1.763834208 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '2.666666667' to each side of the equation. -2.666666667 + 2.666666667 + q = 1.763834208 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + q = 1.763834208 + 2.666666667 q = 1.763834208 + 2.666666667 Combine like terms: 1.763834208 + 2.666666667 = 4.430500875 q = 4.430500875 Simplifying q = 4.430500875

Subproblem 2

q + -2.666666667 = -1.763834208 Simplifying q + -2.666666667 = -1.763834208 Reorder the terms: -2.666666667 + q = -1.763834208 Solving -2.666666667 + q = -1.763834208 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '2.666666667' to each side of the equation. -2.666666667 + 2.666666667 + q = -1.763834208 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + q = -1.763834208 + 2.666666667 q = -1.763834208 + 2.666666667 Combine like terms: -1.763834208 + 2.666666667 = 0.902832459 q = 0.902832459 Simplifying q = 0.902832459

Solution

The solution to the problem is based on the solutions from the subproblems. q = {4.430500875, 0.902832459}

See similar equations:

| 2*sqrt(4x-7)-sqrt(5x+6)=20 | | -3x-4=3x+4 | | 37-8x=6(2-2x)-3 | | X-(x×25/100)=150 | | 2b-3b=5b | | 2b-3b=-1b | | X-(x*25/100)=150 | | 3x^3-54x^2+243x=0 | | 14+x=4x-8 | | 42-50= | | 9a-8a=1a | | 18y+13x=234 | | 14-8x=3(x-8) | | 4=9x-112 | | (x-6)(x-6)=63 | | 3x-40=3x-5 | | 1+lnx-ln(3x)=4lnx | | 22+b=50 | | -4x-8=9x+31 | | .3_1.5/4.9_.5x=1 | | 2m^2+15m-27=0 | | 1+lnx-ln(3x)=4*lnx | | -69=7v-y | | 29+3k=2(7k-2) | | 8+.16=18+.14 | | 3x^3-5x^2+243x=0 | | 6p-9p=24 | | 5n-2=3n | | (8x-5)+(3x+10)+(2x)=46 | | .002-24/x^2=0 | | 11+.10m=21+.08m | | 1186=16tsquared |

Equations solver categories