SOLUTION: Solve the equation. (√5x+39)-8=3x-15 The solution set is ​

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Question 1066684: Solve the equation. (√5x+39)-8=3x-15
The solution set is
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Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your original equation is sqrt(5x + 39) - 8 = 3x - 15

add 8 to both sides of the equation to get sqrt(5x + 39) = 3x - 7

square both sides of the equation to get 5x + 39 = (3x - 7)^2

simplify to get 5x + 39 = 9x^2 - 42x + 49

subtract (5x + 39) from both sides of the equation to get 0 = 9x^2 - 47x + 10

factor the right side of the equation to get 0 = (x - 5) * (9x - 2)

solve for x to get x = 5 or x = 2/9

replace x in your original equation to see if these possible solutions are good.

your original equation is sqrt(5x + 39) - 8 = 3x - 15

when x = 5, this equation becomes sqrt(5*5 + 39) - 8 = 3*5 - 15.

evaluate both sides of this equation to get sqrt(64) - 8 = 15 - 15.

simplify to get 0 = 0

x = 5 is one of the solutions to your original equation.

when x = 2/9, this equation becomes sqrt(5 * 2/9 + 39) - 8 = 3 * 2/9 - 15

evaluate both sides of this equation to get sqrt(10/9 + 39) - 8 = 6/9 - 15

simplify to get 6 and 1/3 = -14 and 1/3.

this is not a true equaation, therefore x = 2/9 is not a solution to your original equation.

the solution to your original equation is x = 5.

you can see this graphically by graphing both equations.

the first equation to graph is y = 3x - 15

the second equation to graph is y = sqrt(5x+39)-8

the graph looks like this:

$$$

the intersection point of the graph of these 2 equations is only at x = 5.