-3q^2-24q+36=0

Simple and best practice solution for -3q^2-24q+36=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^2-24q+36=0 equation: 


Simplifying
-3q2 + -24q + 36 = 0

Reorder the terms:
36 + -24q + -3q2 = 0

Solving
36 + -24q + -3q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + -8q + -1q2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(12 + -8q + -1q2)' equal to zero and attempt to solve:

Simplifying
12 + -8q + -1q2 = 0

Solving
12 + -8q + -1q2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-12 + 8q + q2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 8q + 12 + q2 = 0 + 12

Reorder the terms:
-12 + 12 + 8q + q2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 8q + q2 = 0 + 12
8q + q2 = 0 + 12

Combine like terms: 0 + 12 = 12
8q + q2 = 12

The q term is 8q.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8q + 16 + q2 = 12 + 16

Reorder the terms:
16 + 8q + q2 = 12 + 16

Combine like terms: 12 + 16 = 28
16 + 8q + q2 = 28

Factor a perfect square on the left side:
(q + 4)(q + 4) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(q + 4) equal to 5.291502622 and -5.291502622.


Subproblem 1
q + 4 = 5.291502622

Simplifying
q + 4 = 5.291502622

Reorder the terms:
4 + q = 5.291502622

Solving
4 + q = 5.291502622

Solving for variable 'q'.

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

Add '-4' to each side of the equation.
4 + -4 + q = 5.291502622 + -4

Combine like terms: 4 + -4 = 0
0 + q = 5.291502622 + -4
q = 5.291502622 + -4

Combine like terms: 5.291502622 + -4 = 1.291502622
q = 1.291502622

Simplifying
q = 1.291502622


Subproblem 2
q + 4 = -5.291502622

Simplifying
q + 4 = -5.291502622

Reorder the terms:
4 + q = -5.291502622

Solving
4 + q = -5.291502622

Solving for variable 'q'.

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

Add '-4' to each side of the equation.
4 + -4 + q = -5.291502622 + -4

Combine like terms: 4 + -4 = 0
0 + q = -5.291502622 + -4
q = -5.291502622 + -4

Combine like terms: -5.291502622 + -4 = -9.291502622
q = -9.291502622

Simplifying
q = -9.291502622


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {1.291502622, -9.291502622}
Solution
q = {1.291502622, -9.291502622}

See similar equations:

| 7x-8y=-5fory | | 0.1(x+20)-0.07(x-40)=3 | | v^2-v-12/32-2v^2 | | f(25)=x^2+8x+16 | | 54/6-3*2 | | 4-5(-4n+3)=x | | 4-5(-4+3)=x | | -4(x-10)=-(x-7) | | 0.3(x+20)-0.08(x-50)=14.4 | | 5(t-8)-3(t-7)=13 | | 5(x-5)+4(x-1)=8 | | 10*x^2+20*x+9=0 | | 10x-6=-2x-6 | | 3w+1=100 | | 0=-y^2-70y+1225 | | 3x+x-4=400 | | 3x+x-3=400 | | 0=-y^2-70x+1225 | | 11p^2=19 | | -4p-(1-6p)=x | | 4x-1=400 | | 3x-1=400 | | 7=90-4q | | 3x+99=400 | | 4x+1=400 | | 3x+x+1=400 | | 3x=400+1 | | 8-(x+9)=5-2x | | 3x+1=400x | | 3x+(3x*1)=400 | | 7x-x=x | | 400=3x+(1+3x) |

Equations solver categories