How do you solve using the completing the square method $x^{2} + 8 x + 15 = 0$ $x^2+8x+15=0$ ?

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Answer 1 · 2016-04-11T05:59:11

The solutions for the equation are:
$x = - 3$ $color(green)(x = - 3$ , $x = - 5$ $color(green)(x = -5$

$x^{2} + 8 x + 15 = 0$ $x^2 + 8x + 15 = 0$

$x^{2} + 8 x = - 15$ $x^2 + 8x = -15$

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

$x^{2} + 8 x + 16 = - 15 + 16$ $x^2 + 8x + 16 = - 15 + 16$

$x^{2} + 2 \cdot x \cdot 4 + 4^{2} = 1$ $x^2 + 2 * x * 4 + 4^2 = 1$

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

${(x + 4)}^{2} = 1$ $(x+4)^2 = 1$

$x + 4 = \sqrt{1}$ $x + 4 = sqrt1$ or $x + 4 = - \sqrt{1}$ $x +4 = -sqrt 1$

$x = \sqrt{1} - 4$ $x = sqrt 1 - 4$ or $x = - \sqrt{1} - 4$ $x = -sqrt 1 - 4$

$x = 1 - 4$ $x = 1 - 4$ or $x = - 1 - 4$ $x = -1 - 4$

$x = - 3$ $color(green)(x = - 3$ or $x = - 5$ $color(green)(x = -5$

How do you solve using the completing the square method x^2+8x+15=0x2+8x+15=0x^2+8x+15=0?