Question

Middle term split of x square +2x - 71 = 0

Answer 1

This cannot be done by splitting middle term because -71 is a prime and cannot be factorised into anything other than 1 and 71

Here's the solution by quadratic equation

$x = \frac{ - b \frac{ + }{} \sqrt{ {b}^{2} - 4ac } }{2a} = \frac{ - 2 \frac{ + }{} \sqrt{4 - (4 \times - 71 \times 1)} }{2} \\ x = \frac{ - 2 \frac{ + }{} \sqrt{4 + 284} }{2} \\ x = \frac{ - 2 \frac{ + }{} \sqrt{288} }{2} \\x = \frac{ - 2 \frac{ + }{}12 \sqrt{2} }{2} = - 1 \frac{ + }{} 6 \sqrt{2} \\ \\ therefore \: the \: values \: of \: x \: are \\ x = - 1 + 6 \sqrt{2} \: and - 1 - 6 \sqrt{2}$

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