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

Question

1332 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-13T18:09:31

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

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

$f^{2} - 18 f = - 78$ $f^2 - 18f = - 78$

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

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

$f^{2} - 2 \cdot f \cdot 9 + 9^{2} = 3$ $f^2 - 2 * f * 9 + 9^2 = 3$

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

$f - 9 = \sqrt{3}$ $f-9 = sqrt3$ or $f - 9 = - \sqrt{3}$ $f-9 = -sqrt3$

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

How do you solve f^2 - 18f + 70 = -8f2−18f+70=−8f^2 - 18f + 70 = -8 by completing the square?