If twelve is added to six times a number, the result is twenty-eight less than the square of the number. Find all such numbers.

Question
If twelve is added to six times a number, the result is twenty-eight less than the square of the number. Find all such numbers.

Answers (1)

2021-02-23
Let x be the number so we write the equation: \(\displaystyle{6}{x}+{12}={x}^{{2}}-{28}\)
Write in the form \(\displaystyle{a}{x}^{{2}}+{b}{x}+{c}={0}\)
\(\displaystyle{0}={x}^{{2}}-{6}{x}-{40}\)
Factor the right side: 0=(x+4)(x-10)
By zero product property, x+4=0,x-10=0 x=-4,10
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