need to solve 22-Q=Q^2-17Q+50?

Question

This is a margial revenue /marginal cost problem. need to know how to solve this having a brainfart. Got the answer with a calculator but i need to be able to solve it algebraically.

Answer 1

0=q^2-16q+28
0=(q-2)(q-14)
q=2,14

Answer 2

Simplifying
22 + -1Q = Q2 + -17Q + 50

Reorder the terms:
22 + -1Q = 50 + -17Q + Q2

Solving
22 + -1Q = 50 + -17Q + Q2

Solving for variable 'Q'.

Reorder the terms:
22 + -50 + -1Q + 17Q + -1Q2 = 50 + -17Q + Q2 + -50 + 17Q + -1Q2

Combine like terms: 22 + -50 = -28
-28 + -1Q + 17Q + -1Q2 = 50 + -17Q + Q2 + -50 + 17Q + -1Q2

Combine like terms: -1Q + 17Q = 16Q
-28 + 16Q + -1Q2 = 50 + -17Q + Q2 + -50 + 17Q + -1Q2

Reorder the terms:
-28 + 16Q + -1Q2 = 50 + -50 + -17Q + 17Q + Q2 + -1Q2

Combine like terms: 50 + -50 = 0
-28 + 16Q + -1Q2 = 0 + -17Q + 17Q + Q2 + -1Q2
-28 + 16Q + -1Q2 = -17Q + 17Q + Q2 + -1Q2

Combine like terms: -17Q + 17Q = 0
-28 + 16Q + -1Q2 = 0 + Q2 + -1Q2
-28 + 16Q + -1Q2 = Q2 + -1Q2

Combine like terms: Q2 + -1Q2 = 0
-28 + 16Q + -1Q2 = 0

Factor a trinomial.
(-14 + Q)(2 + -1Q) = 0

Subproblem 1Set the factor '(-14 + Q)' equal to zero and attempt to solve:

Simplifying
-14 + Q = 0

Solving
-14 + Q = 0

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

Add '14' to each side of the equation.
-14 + 14 + Q = 0 + 14

Combine like terms: -14 + 14 = 0
0 + Q = 0 + 14
Q = 0 + 14

Combine like terms: 0 + 14 = 14
Q = 14

Simplifying
Q = 14
Subproblem 2Set the factor '(2 + -1Q)' equal to zero and attempt to solve:

Simplifying
2 + -1Q = 0

Solving
2 + -1Q = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1Q = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1Q = 0 + -2
-1Q = 0 + -2

Combine like terms: 0 + -2 = -2
-1Q = -2

Divide each side by '-1'.
Q = 2

Simplifying
Q = 2

Solution Q = {14, 2}

Answer 3

22-Q=Q^2-17Q+50
Q² - 17Q + 50 - 22 + Q = 0
Q² - 16Q + 28 = 0
delta = 256 - 4.1.28
delta = 256 - 112
delta = 144

q = (16 +/- \/144) : 2
Q' = (16 + 12) : 2
Q' = 28 : 2 =14
Q" = (16 - 12) : 2
Q" = 4 : 2 = 2
Solution: Q = 2 or 14.
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Answer 4

1. Move all terms to one side of the equation

-22+Q+Q^2-17Q+50 = 0

2. combine like terms Q^2-16Q+28=0

3. solve using the quadratic formula

Q =[ -B+or- Sqrt (B^2-4AC)]/2A

A is the coef of Q^2, B the coef of Q and C is the constant.

I'll permit you to do the arithmetic

Answer 5

22-Q = Q^2 - 17Q+50
22 -50 = Q+Q^2-17Q
-28 = -16Q+Q^2
-28 = Q(-16+Q)

Arghh, I'm blocked.. sorry :-p

Isn't it needed to have a second line to solve this ?

Answer 6

22-Q=Q^2-17Q+50
Move things aroung a little
0 = Q^2-16Q+28
factor
(Q-14)(Q-2)= 0
then,
Q = 14 and Q =2

Answer 7

22 - Q = Q² - 17Q + 50
Q² -16Q + 28 = 0
(Q - 14)(Q - 2) = 0

Q = 2 or 14

Answer 8

22-Q+Q=Q^2-17Q+Q+50
22=Q^2-16Q+50
22-22=Q^2-16Q+50-22
0=Q^2-16Q+28
0=(Q-2)(Q-14)
Q=2 Q=14

Answer 9

first of all put all the variables and numerals on one side of the equals sign--> 0=Q^2-16Q+28 you should be able to figure it out from there.