2q(q-3)=9

Simple and best practice solution for 2q(q-3)=9 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 2q(q-3)=9 equation:


Simplifying
2q(q + -3) = 9

Reorder the terms:
2q(-3 + q) = 9
(-3 * 2q + q * 2q) = 9
(-6q + 2q2) = 9

Solving
-6q + 2q2 = 9

Solving for variable 'q'.

Reorder the terms:
-9 + -6q + 2q2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + -6q + 2q2 = 0

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

Divide each side by '2'.
-4.5 + -3q + q2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -3q + 4.5 + q2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -3q + q2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -3q + q2 = 0 + 4.5
-3q + q2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-3q + q2 = 4.5

The q term is -3q.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3q + 2.25 + q2 = 4.5 + 2.25

Reorder the terms:
2.25 + -3q + q2 = 4.5 + 2.25

Combine like terms: 4.5 + 2.25 = 6.75
2.25 + -3q + q2 = 6.75

Factor a perfect square on the left side:
(q + -1.5)(q + -1.5) = 6.75

Calculate the square root of the right side: 2.598076211

Break this problem into two subproblems by setting 
(q + -1.5) equal to 2.598076211 and -2.598076211.

Subproblem 1

q + -1.5 = 2.598076211 Simplifying q + -1.5 = 2.598076211 Reorder the terms: -1.5 + q = 2.598076211 Solving -1.5 + q = 2.598076211 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + q = 2.598076211 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + q = 2.598076211 + 1.5 q = 2.598076211 + 1.5 Combine like terms: 2.598076211 + 1.5 = 4.098076211 q = 4.098076211 Simplifying q = 4.098076211

Subproblem 2

q + -1.5 = -2.598076211 Simplifying q + -1.5 = -2.598076211 Reorder the terms: -1.5 + q = -2.598076211 Solving -1.5 + q = -2.598076211 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + q = -2.598076211 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + q = -2.598076211 + 1.5 q = -2.598076211 + 1.5 Combine like terms: -2.598076211 + 1.5 = -1.098076211 q = -1.098076211 Simplifying q = -1.098076211

Solution

The solution to the problem is based on the solutions from the subproblems. q = {4.098076211, -1.098076211}

See similar equations:

| 10p+30=180 | | b/4-25=650 | | (2x^2-x+7)-(x-1)= | | 4h+18=30 | | x+6=123/4 | | 1114+4=19a+10 | | -112=-28q | | 3(10-3)= | | 2+r/3=-23 | | (6x+1)/2=(x+5)/4+(x-3)/4 | | -3z+2.8=8.8 | | 1114+4a=18 | | 1114+4a=19 | | -6x+52-8(x-1)=4x-(7x-5)-2x+1 | | 3/5+7/5x=2/x^2 | | 1114+4=19 | | 3x^2+29x-56=0 | | 16*x^2+144x+384=0 | | 7z-23=-8+4z | | 4p-11=-17+3p | | 3p+13q=-24 | | (x^2+11x+33)/(x+7) | | -0.5*32x^2+32x+12=24 | | 6(5x-2x)=78 | | -1/2*32x^2+32x+12 | | ax-ax+az= | | -1/2*32x^2+32x+12=0 | | 8x-14= | | 5x-14= | | 8784/48 | | 0.9y=139 | | (y+3)(y-3)-y(y+5)=6 |

Equations solver categories