How do you solve the quadratic equation by completing the square: $x^2+18x+67=0$ ?

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Answer 1 · 2015-07-19T13:52:54

$color(green)(x = sqrt 14 -9$ or $color(green)(x = -sqrt 14 -9$

$x^2 + 18x = -67$

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

$x^2 + 18x + 81 = -67 + 81$

$x^2 + 2*x*9 + 9^2 = 14$

Using the Identity $color(blue)((a+b)^2 = a^2 + 2ab + b^2$ , we get
$(x+9)^2 = 14$
$x + 9 = sqrt14$ or $x +9 = -sqrt14$

$color(green)(x = sqrt 14 -9$ or $color(green)(x = -sqrt 14 -9$

How do you solve the quadratic equation by completing the square: x^2+18x+67=0x^2+18x+67=0?