SOLUTION: Solve the equation: 18(𝑥−2) = 1 + ((20)/(𝑥+2)) Thank you!

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Question 1125476: Solve the equation:
18(𝑥−2) = 1 + ((20)/(𝑥+2))
Thank you!
Found 3 solutions by josgarithmetic, Alan3354, Theo:
Answer by josgarithmetic(39799) About Me  (Show Source):
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
18(x-2) = 1 + (20)/(x+2)
Multiply thru by x+2
18(x-2)*(x+2) = x+2 + 20
18(x^2-4) = x + 22
18x^2 - 72 = x + 22
18x^2 - x - 94 = 0
Can you do the rest?

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your equation is 18 * (x-2) = 1 + (20 / (x + 2))

multiply both sides of this equation by (x + 2) to get:

18 * (x-2) * (x+2) = (x + 2) + 20

(x-2) * (x+2) is equal to (x^2 - 4)

equation becomes:

18 * (x^2 - 4) = (x + 2) + 20

simplify to get 18 * x^2 - 72 = x + 22

subtract x + 22 from both sides of the equation to get:

x^2 - 72 - x - 22 = 0

combine like terms to get:

x^2 - x - 94 = 0

factor this quadratic equation to get:

x = 2.313164797 or x = -2.257609241

that's your solution.

you can show that this is true graphically as shown below:

$$$

the red line is 18 * (x - 2).

the blue line is 1 + (20 / (x + 2)).

the solution is the intersection of those two lines.

x = 2.313164797 or x = -2.257609241 rounds to x = 2.313 or x = -2.258 as shown on the graph.