How do you complete the square to solve $x^{2} + 6 x + 34 = 0$ $x^2 + 6x + 34 = 0$ ?

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How do you complete the square to solve $x^{2} + 6 x + 34 = 0$ $x^2 + 6x + 34 = 0$ ?

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Answer 1 · 2015-06-07T13:45:26

$x^{2} + 6 x + 34 = 0$ $x^2+6x+34 = 0$
can be written as
$XXXX$ $color(white)("XXXX")$ $x^{2} + 6 x = - 34$ $x^2+6x = -34$

completing the square:
$XXXX$ $color(white)("XXXX")$ $x^{2} + 6 x + 9 = - 25$ $x^2+6x+9 = -25$
$XXXX$ $color(white)("XXXX")$ ${(x + 3)}^{2} = - 25$ $(x+3)^2 = -25$
take the square root of both sides
$XXXX$ $color(white)("XXXX")$ $x + 3 = \sqrt{- 25}$ $x+3 = sqrt(-25)$ $XXXX$ $color(white)("XXXX")$ (Note: no Real solutions)

$XXXX$ $color(white)("XXXX")$ $x = - 3 \pm 5 i$ $x= -3 +-5i$

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How do you complete the square to solve $x^{2} + 6 x + 34 = 0$ $x^2 + 6x + 34 = 0$ ?

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How do you complete the square to solve x^2 + 6x + 34 = 0x2+6x+34=0x^2 + 6x + 34 = 0?

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How do you complete the square to solve $x^{2} + 6 x + 34 = 0$ $x^2 + 6x + 34 = 0$ ?