How do you solve $f^2 - 18f + 70 = -8$ by completing the square?

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Answer 1 · 2016-05-13T18:09:31

The solutions are:
$color(green)(f= sqrt 3 + 9$ , $color(green)(f = -sqrt 3 +9$

$f^2 - 18f + 70 = - 8$

$f^2 - 18f = - 78$

To write the Left Hand Side as a Perfect Square, we add 81 to both sides:

$f^2 - 18f + 81 = - 78 + 81$

$f^2 - 2 * f * 9 + 9^2 = 3$

Using the Identity $color(blue)((a-b)^2 = a^2 - 2ab + b^2$ , we get
$( f - 9)^2 = 3$

$f-9 = sqrt3$ or $f-9 = -sqrt3$

$color(green)(f= sqrt 3 + 9$ , $color(green)(f = -sqrt 3 +9$

How do you solve f^2 - 18f + 70 = -8f^2 - 18f + 70 = -8 by completing the square?