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salantis [7]
3 years ago
14

Which of the following tables shows the correct steps to transform x2 + 10x + 24 = 0 into the form (x − p)2 = q?

Mathematics
1 answer:
Leona [35]3 years ago
3 0

x^2+10x+24=0


\text{Use:}\\a^2+2ab+b^2=(a+b)^2


x^2+10x+24=x^2+2\cdot x\cdot5+24


\text{OK. We have}\\a^2=x^2\\2ab=2\cdot x\cdot5\to b=5\\\text{therefore}\ b^2\ \text{must be equal}\ 25=5^2.\\\text{we have:} 24. \text{We have to increase it by 1}\\ \text{Therefore the correct steps are in answer D.}


D.\ Step1\\x^2+10x+24=0\\\\x^2+2\cdot x\cdot5+24=0\\\\x^2+2\cdot x\cdot5+24+1=0+1\\\\Step2\\\\x^2+2\cdot x\cdot5+25=1\\\\x^2+2\cdot x\cdot5+5^2=1\\\\Step3\\\\(x+5)^2=1

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