600-32q=q^2-56q+422

Simple and best practice solution for 600-32q=q^2-56q+422 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 600-32q=q^2-56q+422 equation:


Simplifying
600 + -32q = q2 + -56q + 422

Reorder the terms:
600 + -32q = 422 + -56q + q2

Solving
600 + -32q = 422 + -56q + q2

Solving for variable 'q'.

Reorder the terms:
600 + -422 + -32q + 56q + -1q2 = 422 + -56q + q2 + -422 + 56q + -1q2

Combine like terms: 600 + -422 = 178
178 + -32q + 56q + -1q2 = 422 + -56q + q2 + -422 + 56q + -1q2

Combine like terms: -32q + 56q = 24q
178 + 24q + -1q2 = 422 + -56q + q2 + -422 + 56q + -1q2

Reorder the terms:
178 + 24q + -1q2 = 422 + -422 + -56q + 56q + q2 + -1q2

Combine like terms: 422 + -422 = 0
178 + 24q + -1q2 = 0 + -56q + 56q + q2 + -1q2
178 + 24q + -1q2 = -56q + 56q + q2 + -1q2

Combine like terms: -56q + 56q = 0
178 + 24q + -1q2 = 0 + q2 + -1q2
178 + 24q + -1q2 = q2 + -1q2

Combine like terms: q2 + -1q2 = 0
178 + 24q + -1q2 = 0

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

Divide each side by '-1'.
-178 + -24q + q2 = 0

Move the constant term to the right:

Add '178' to each side of the equation.
-178 + -24q + 178 + q2 = 0 + 178

Reorder the terms:
-178 + 178 + -24q + q2 = 0 + 178

Combine like terms: -178 + 178 = 0
0 + -24q + q2 = 0 + 178
-24q + q2 = 0 + 178

Combine like terms: 0 + 178 = 178
-24q + q2 = 178

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 = 178 + 144

Reorder the terms:
144 + -24q + q2 = 178 + 144

Combine like terms: 178 + 144 = 322
144 + -24q + q2 = 322

Factor a perfect square on the left side:
(q + -12)(q + -12) = 322

Calculate the square root of the right side: 17.944358445

Break this problem into two subproblems by setting 
(q + -12) equal to 17.944358445 and -17.944358445.

Subproblem 1

q + -12 = 17.944358445 Simplifying q + -12 = 17.944358445 Reorder the terms: -12 + q = 17.944358445 Solving -12 + q = 17.944358445 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 = 17.944358445 + 12 Combine like terms: -12 + 12 = 0 0 + q = 17.944358445 + 12 q = 17.944358445 + 12 Combine like terms: 17.944358445 + 12 = 29.944358445 q = 29.944358445 Simplifying q = 29.944358445

Subproblem 2

q + -12 = -17.944358445 Simplifying q + -12 = -17.944358445 Reorder the terms: -12 + q = -17.944358445 Solving -12 + q = -17.944358445 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 = -17.944358445 + 12 Combine like terms: -12 + 12 = 0 0 + q = -17.944358445 + 12 q = -17.944358445 + 12 Combine like terms: -17.944358445 + 12 = -5.944358445 q = -5.944358445 Simplifying q = -5.944358445

Solution

The solution to the problem is based on the solutions from the subproblems. q = {29.944358445, -5.944358445}

See similar equations:

| -15+18=m-8 | | 269x^2-9=0 | | 4+4+2.5=c | | -32x^2=4x | | 0=-4y^2-12y-5 | | 9(4p+12)-15p=3 | | k^2-4k=0 | | 2z+2=7 | | 6x+-2+2x=-2+8 | | 178=q^2-24q | | 5-3y=2y-10 | | 3p-9=6-2p | | 200x^2+1600=0 | | 144x^2-2x-122=0 | | 2n^2-2n=0 | | a(-12+a)=0 | | -7n+n^2=0 | | x^3-18x^2+80x=0 | | w(9+w)=0 | | 6s^2-7s+1= | | x=6y-4 | | 4x^2-6x-15=0 | | 6y-4= | | -2y+28= | | -3x-(5y-3)=-21 | | 5x^2=33x+56 | | y=-1.25(0)+5 | | y=-1.25x+5 | | x+x+2+x=24 | | (x+6)(x-5)=42 | | 0=1.25x+20 | | 0.50x+0.70(50)=0.25(120) |

Equations solver categories