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)
Will give best response to first to help, and fan all who helps.
what is half of 12?
6...
what is half of -12 actually ..
what is \(6^2\) ?
6^2 = 36, half of -12 is -6,
therefore you need to put \(36\) for "what" in \[t^2 - 12 + (What) \]
Ok so it would be t^2 - 12 + 36?
yes it is a perfect square, it is \((t-6)^2\)
Ok thanks what about for #3 & #5 how do I solve those?
\[x^2− 10x − 21 = 0\] 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 \[(x-5)^2=21+25=46\]
then take the square root of both sides, get \[x-5\sqrt{46}\] or \[x-5=-\sqrt{46}\]
solve for \(x\) by adding 5 and get \[x=5\pm\sqrt{46}\]
\[x = \sqrt{46} + 5, 5 - \sqrt{46}\] So is this the answer?
oh i mean "yes"
Ok thanks, can you help me with #5 as well please. :)
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