q^2+4q+8=2q^2-20q+68

Simple and best practice solution for q^2+4q+8=2q^2-20q+68 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 q^2+4q+8=2q^2-20q+68 equation:


Simplifying
q2 + 4q + 8 = 2q2 + -20q + 68

Reorder the terms:
8 + 4q + q2 = 2q2 + -20q + 68

Reorder the terms:
8 + 4q + q2 = 68 + -20q + 2q2

Solving
8 + 4q + q2 = 68 + -20q + 2q2

Solving for variable 'q'.

Reorder the terms:
8 + -68 + 4q + 20q + q2 + -2q2 = 68 + -20q + 2q2 + -68 + 20q + -2q2

Combine like terms: 8 + -68 = -60
-60 + 4q + 20q + q2 + -2q2 = 68 + -20q + 2q2 + -68 + 20q + -2q2

Combine like terms: 4q + 20q = 24q
-60 + 24q + q2 + -2q2 = 68 + -20q + 2q2 + -68 + 20q + -2q2

Combine like terms: q2 + -2q2 = -1q2
-60 + 24q + -1q2 = 68 + -20q + 2q2 + -68 + 20q + -2q2

Reorder the terms:
-60 + 24q + -1q2 = 68 + -68 + -20q + 20q + 2q2 + -2q2

Combine like terms: 68 + -68 = 0
-60 + 24q + -1q2 = 0 + -20q + 20q + 2q2 + -2q2
-60 + 24q + -1q2 = -20q + 20q + 2q2 + -2q2

Combine like terms: -20q + 20q = 0
-60 + 24q + -1q2 = 0 + 2q2 + -2q2
-60 + 24q + -1q2 = 2q2 + -2q2

Combine like terms: 2q2 + -2q2 = 0
-60 + 24q + -1q2 = 0

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

Divide each side by '-1'.
60 + -24q + q2 = 0

Move the constant term to the right:

Add '-60' to each side of the equation.
60 + -24q + -60 + q2 = 0 + -60

Reorder the terms:
60 + -60 + -24q + q2 = 0 + -60

Combine like terms: 60 + -60 = 0
0 + -24q + q2 = 0 + -60
-24q + q2 = 0 + -60

Combine like terms: 0 + -60 = -60
-24q + q2 = -60

The q term is -24q.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24q + 144 + q2 = -60 + 144

Reorder the terms:
144 + -24q + q2 = -60 + 144

Combine like terms: -60 + 144 = 84
144 + -24q + q2 = 84

Factor a perfect square on the left side:
(q + -12)(q + -12) = 84

Calculate the square root of the right side: 9.16515139

Break this problem into two subproblems by setting 
(q + -12) equal to 9.16515139 and -9.16515139.

Subproblem 1

q + -12 = 9.16515139 Simplifying q + -12 = 9.16515139 Reorder the terms: -12 + q = 9.16515139 Solving -12 + q = 9.16515139 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + q = 9.16515139 + 12 Combine like terms: -12 + 12 = 0 0 + q = 9.16515139 + 12 q = 9.16515139 + 12 Combine like terms: 9.16515139 + 12 = 21.16515139 q = 21.16515139 Simplifying q = 21.16515139

Subproblem 2

q + -12 = -9.16515139 Simplifying q + -12 = -9.16515139 Reorder the terms: -12 + q = -9.16515139 Solving -12 + q = -9.16515139 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + q = -9.16515139 + 12 Combine like terms: -12 + 12 = 0 0 + q = -9.16515139 + 12 q = -9.16515139 + 12 Combine like terms: -9.16515139 + 12 = 2.83484861 q = 2.83484861 Simplifying q = 2.83484861

Solution

The solution to the problem is based on the solutions from the subproblems. q = {21.16515139, 2.83484861}

See similar equations:

| 3(-2x+7)=-6x-22 | | 0.4+2.5=0.2x-4 | | 4x^2-26x=-5x^2-6x-4 | | 11(x-2)=7x-2 | | -18+4+x=4-19 | | 7-x=3(2x-1) | | 38+7x=4x+8 | | x*x-12x+25=0 | | 8+4(p-4)=2(2p-8) | | 3(n-2)=n+2 | | (2x^2-1)+(-2)=4 | | 11x=35-4 | | -8(1-5x)=75 | | 2*1.333+14=6-4*1.333 | | 12+28=x | | (6x)-7=4x+4 | | 2x^2-3=4 | | b-7+7b=18 | | 109.3-184.9= | | 2(5-3y)-5(y+11)=10-3(5y-1) | | -8(1-5)=75 | | y=20-400 | | x^4-3x+35= | | -7(11c+4)= | | 10x-8=5x+23 | | 14+8=y | | 5(1+2u)=25 | | 2(w-6)=6w+24 | | 0=1x^2+19X+48 | | 500*.12*2= | | -x^2=9x | | -5(7q-6)=65 |

Equations solver categories