30x2 – 45xy – 10x =
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Question: you solve and check this problem 30x2 – 45xy – 10x = .

I'm not too sure what it is that you want done here, but I've done some work on the problem, I hope that it helps.

30x^2 - 45xy - 10x = 0

30x^2 - 5(y+2)x = 0        --  multiply by 4 times the x^2-coefficient, i.e. 120

3600 - 600(9y+2)x = 0    --  now add and subtract the square of the x-coefficient, i.e. [5(9y+2)]^2.

3600 - 600(9y+2)x + 5^2(9y+2)^2 = 25(9y+2)^2 = 0   -- note that we have completed the square.

(60x - 5(9y+2))^2 = 25(9y+2)^2    -- take square root of both sides.

60x - 5(9y+2) = ± 5(9y+2)

if lhs = -5(9y+2),  then x = 0   -- ignore this solution.

if lhs = +5(9y+2),   then

60x = 10(9y+2)

6x = 9y + 2

y = (1/9)(6x - 2)

Answer: solutions to the original quadratic expression are any points lying on the line: y = (1/9)(6x - 2)

by Level 11 User (81.5k points)

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