How do you solve $x^2+8x=9$ by completing the square?

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Answer 1 · 2016-04-26T14:39:19

The solutions are:
$color(green)(x = 1 , x=-9$

$x^2 + 8x = 9$

To write the Left Hand Side as a Perfect Square, we add 16 to both sides:

$x^2 + 8x + 16 = 9+ 16$

$x^2 + 2* x * 4 + 4^2 = 25$

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

$(x+4)^2 = 25$

$x + 4 = sqrt25$ or $x +4 = -sqrt25$

$x + 4 = 5$ , $x +4 = -5$

$x = 5- 4 =1$ ,

$x = -5 -4 = -9$

The solutions are:
$color(green)(x = 1 , x=-9$

How do you solve x^2+8x=9x^2+8x=9 by completing the square?