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Mathematics 23 Online
OpenStudy (leozap1):

1. Complete the square. t^2 - 12 + (What) 3. x^2− 10x − 21 = 0 5. Use the discriminant to determine whether the equation has two distinct real solutions, a single real solution, or no real solutions. -3x + 2x - 2 = 0 (I did the rest of them thats why it skips some numbers)

OpenStudy (leozap1):

Will give best response to first to help, and fan all who helps.

OpenStudy (anonymous):

what is half of 12?

OpenStudy (leozap1):

6...

OpenStudy (shamil98):

what is half of -12 actually ..

OpenStudy (anonymous):

what is \(6^2\) ?

OpenStudy (leozap1):

6^2 = 36, half of -12 is -6,

OpenStudy (anonymous):

therefore you need to put \(36\) for "what" in \[t^2 - 12 + (What) \]

OpenStudy (leozap1):

Ok so it would be t^2 - 12 + 36?

OpenStudy (anonymous):

yes it is a perfect square, it is \((t-6)^2\)

OpenStudy (leozap1):

Ok thanks what about for #3 & #5 how do I solve those?

OpenStudy (anonymous):

\[x^2− 10x − 21 = 0\] complete the square start with \[x^2-10x=21\] then make the left hand side a perfect square by adding \(25\) as befoer (half of 10 is 5, 5 squared is 25) and write \[(x-5)^2=21+25=46\]

OpenStudy (anonymous):

then take the square root of both sides, get \[x-5\sqrt{46}\] or \[x-5=-\sqrt{46}\]

OpenStudy (anonymous):

solve for \(x\) by adding 5 and get \[x=5\pm\sqrt{46}\]

OpenStudy (leozap1):

\[x = \sqrt{46} + 5, 5 - \sqrt{46}\] So is this the answer?

OpenStudy (anonymous):

oh i mean "yes"

OpenStudy (leozap1):

Ok thanks, can you help me with #5 as well please. :)

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