Find the two consecutive numbers whose squares have the sum 85 by quadratic equation formula)

Let the number $x\\$

and its consecutive number $= x + 1 \\$

According to the question,

$x ^{2} + (x + 1)^{2} = 85 \\ \Rightarrow x^{2} + x^{2} + 1 + 2x = 85\\ \Rightarrow 2x^{2} + 2x -84 = 0 \\ \Rightarrow x^{2} + x - 42 = 0 \\ \Rightarrow x^{2} + 7x - 6x - 42 = 0 \\ \Rightarrow(x -6) (x+7) = 0 \\ \Rightarrow x= 6, x = -7 \\$

then two consecutive number   $x = 6, (x + 1) = 6 +1 = 7 \\$

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