SOLUTION: Please help me solve the following: Solve for x: 9𝑥^2 − 24𝑥 = −16 Thank you!

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Question 1094659: Please help me solve the following:
Solve for x: 9𝑥^2 − 24𝑥 = −16



Thank you!
Found 3 solutions by josgarithmetic, greenestamps, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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9x%5E2-24x%2B16=0
x=%2824%2B-+sqrt%2824%5E2-4%2A9%2A16%29%29%2F%282%2A9%29
* x=%2824%2B-+sqrt%28576-576%29%29%2F%282%2A9%29
x=24%2F%282%2A9%29
x=12%2F9
highlight%28x=4%2F3%29

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Notice also that 9x^2 is a square term and 16 is a square term, so you might be able to pick a factorization and check it. Maybe this could work:
%283x-4%29%283x-4%29
F.O.I.L. Method,
9x%5E2-12x-12x%2B16
9x%5E2-24x%2B16
Same as the trinomial expression found earlier, so you would have
%283x-4%29%5E2=0--------obviously x=4%2F3.





* fixed sign mistake

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

Of course you first need to get all the terms on one side of the equation, with 0 on the other side.

After that, there are certain factoring patterns you should learn to recognize, so you can do the work faster.

Look at the first and last terms of your equation: 9x^2 and 16. Those are both perfect squares: 9x^2 = (3x)^2 and 16 = 4^2.

Then with a negative middle term, you only need to check to see if (3x-4)^2 gives you the correct middle term. It does... so
9x%5E2-24x%2B16+=+0
%283x-4%29%5E2+=+0
3x-4+=+0
3x+=+4
x+=+4%2F3

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me solve the following:
Solve for x: 9𝑥^2 − 24𝑥 = −16
Thank you!
9x%5E2+-+24x+=+-+16

9x%5E2+-+24x+%2B+16+=+0

9x%5E2+-+12x+-+12x+%2B+16+=+0 ------ Replcing - 24x with - 12x - 12x 

3x(3x - 4) - 4(3x - 4) = 0

%283x+-+4%29%5E2+=+0

3x - 4 = 0

3x = 4

highlight_green%28matrix%281%2C5%2C+x%2C+%22=%22%2C+4%2F3%2C+%22or%22%2C+1%261%2F3%29%29

BE AWARE: The answer IS NOT -+4%2F3