How do you solve x^2-10x-9=0?

1 Answer
George C.
Dec 13, 2016

x = 5+-sqrt(34)

Explanation:

The difference of squares identity can be written:

a^2-b^2 = (a-b)(a+b)

Use this with a = (x-5) and b=sqrt(34) as follows:

0 = x^2-10x-9

color(white)(0) = x^2-10x+25-34

color(white)(0) = (x-5)^2-(sqrt(34))^2

color(white)(0) = ((x-5)-sqrt(34))((x-5)+sqrt(34))

color(white)(0) = (x-5-sqrt(34))(x-5+sqrt(34))

Hence x = 5+-sqrt(34)

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