Question

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

Answer 1

$x^2+10x+24=0$

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

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

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

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