How do you solve $x^{2} + 6 x + 7 = 0$ $x^2 + 6x + 7 = 0$ by completing the square?

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Answer 1 · 2015-05-05T12:20:03

Note that $x^{2} + 6 x + 9 = {(x + 3)}^{2}$ $color(red)(x^2+6x+9) = color(blue)((x+3)^2)$

Given $x^{2} + 6 x + 7 = 0$ $x^2+6x+7=0$
we can rewrite this as
$x^{2} + 6 x + 9 - 2 = 0$ $color(red)(x^2+6x+9) -2 = 0$

${(x + 3)}^{2} = 2$ $color(blue)((x+3)^2) = 2$

$x + 3 = \pm \sqrt{2}$ $x+3 = +-sqrt(2)$

$x = - 3 \pm \sqrt{2}$ $x=-3+-sqrt(2)$

How do you solve x2+6x+7=0x^2 + 6x + 7 = 0 by completing the square?