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

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Answer 1 · 2016-03-30T16:27:48

The solutions are :
$color(green)(x = 5$ or $color(green)(x = 3$

$x^2 - 8x +15= 0$

$x^2 - 8x = - 15$

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

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

$x^2 - 2*x*4 + 4^2 = 1$

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

$(x-4)^2 = 1$

$x - 4 = sqrt1$ or $x -4 = -sqrt1$

$color(green)(x = 1 + 4 = 5$ or $color(green)(x = - 1 + 4 = 3$

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