How do you solve the quadratic equation by completing the square: $r^2 + 14r = -13$ ?

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Answer 1 · 2015-07-16T08:26:37

The solutions for the equation are:
$color(blue)(r = -1 , r=-13$

$r^2 +14r = -13$

To write the Left Hand Side as a Perfect Square, we add 49 to both sides
$r^2 +14r +49 = -13+49$

$r^2 +14r +49 = 36$

Using the Identity $color(blue)((a+b)^2 = a^2 + 2ab + b^2$ , we get
$(r+7)^2 = 36$

$r + 7 = sqrt36$ or $r +7 = -sqrt36$

$r + 7 = 6$ or $r +7 = -6$

$color(blue)(r = -1 or r=-13$

How do you solve the quadratic equation by completing the square: r^2 + 14r = -13r^2 + 14r = -13?