3q^2-11=20q

Simple and best practice solution for 3q^2-11=20q 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^2-11=20q equation: 


Simplifying
3q2 + -11 = 20q

Reorder the terms:
-11 + 3q2 = 20q

Solving
-11 + 3q2 = 20q

Solving for variable 'q'.

Reorder the terms:
-11 + -20q + 3q2 = 20q + -20q

Combine like terms: 20q + -20q = 0
-11 + -20q + 3q2 = 0

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

Divide each side by '3'.
-3.666666667 + -6.666666667q + q2 = 0

Move the constant term to the right:

Add '3.666666667' to each side of the equation.
-3.666666667 + -6.666666667q + 3.666666667 + q2 = 0 + 3.666666667

Reorder the terms:
-3.666666667 + 3.666666667 + -6.666666667q + q2 = 0 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + -6.666666667q + q2 = 0 + 3.666666667
-6.666666667q + q2 = 0 + 3.666666667

Combine like terms: 0 + 3.666666667 = 3.666666667
-6.666666667q + q2 = 3.666666667

The q term is -6.666666667q.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667q + 11.11111112 + q2 = 3.666666667 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667q + q2 = 3.666666667 + 11.11111112

Combine like terms: 3.666666667 + 11.11111112 = 14.777777787
11.11111112 + -6.666666667q + q2 = 14.777777787

Factor a perfect square on the left side:
(q + -3.333333334)(q + -3.333333334) = 14.777777787

Calculate the square root of the right side: 3.844187533

Break this problem into two subproblems by setting 
(q + -3.333333334) equal to 3.844187533 and -3.844187533.


Subproblem 1
q + -3.333333334 = 3.844187533

Simplifying
q + -3.333333334 = 3.844187533

Reorder the terms:
-3.333333334 + q = 3.844187533

Solving
-3.333333334 + q = 3.844187533

Solving for variable 'q'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + q = 3.844187533 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + q = 3.844187533 + 3.333333334
q = 3.844187533 + 3.333333334

Combine like terms: 3.844187533 + 3.333333334 = 7.177520867
q = 7.177520867

Simplifying
q = 7.177520867


Subproblem 2
q + -3.333333334 = -3.844187533

Simplifying
q + -3.333333334 = -3.844187533

Reorder the terms:
-3.333333334 + q = -3.844187533

Solving
-3.333333334 + q = -3.844187533

Solving for variable 'q'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + q = -3.844187533 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + q = -3.844187533 + 3.333333334
q = -3.844187533 + 3.333333334

Combine like terms: -3.844187533 + 3.333333334 = -0.510854199
q = -0.510854199

Simplifying
q = -0.510854199


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {7.177520867, -0.510854199}

See similar equations:

| 0=-5t+10t | | 4=6(x+8)-3x | | 3(k-5)-2(k+1)-13=-22 | | -22=-11k | | 2(x*x)+13x+84=0 | | 14a^2-18a-20=0 | | -5m+0.50=11.50 | | 12(3x+15x)+38=208 | | -5(4-7x)=400 | | x^4=2560x | | 0.30x+2.5=0.70 | | -7=d+21 | | 0.5(x+2)-.07(x+2)=-0.2x-.4 | | .3x+(x-20)+40+(x-10)=360 | | 3r+25=6 | | 9x+11-4x+3=24 | | 3(5+7+x)= | | 6(3x+6)=36 | | 6.1+1.4n=3.16 | | 9=k+13 | | 61=(3x+7)+(5x-2) | | 19=b+3 | | x/2-1=23 | | 36-(-4x)=-1 | | x(x-6)=280 | | 7+(3+5)=x+8 | | R+11=-2 | | 12x^3=20x^3+48x | | 61=(3x+7)+(5x-3) | | 18c^2-3c-10=0 | | 4.9t^2+t-14=0 | | R+45=-8 |

Equations solver categories