How do you solve the quadratic equation by completing the square: $x^2 – 8x + 12 = 0$ ?

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How do you solve the quadratic equation by completing the square: $x^2 – 8x + 12 = 0$ ?

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Answer 1 · 2015-07-13T09:15:37

Work out which factors of 12 add together to give 8. You can then factorise the equation. 12 is either $3*4$ or $6*2$ - $3+4 = 7$ so that won't work, but $6 + 2 = 8$ so that does work.

Explanation:

$(x - 6)(x-2) = 0$

Answer 2 · 2015-07-13T12:49:34

$x=6$ or $x=2$
$color(white)("XXXX")$ (solved by completion of squares method)

Explanation:

Given $x^2–8x+12=0$

$color(white)("XXXX")$ Move the constant to the right side
$x^2-8x = -12$
$color(white)("XXXX")$ If $x^2$ and $-8x$ are the first two terms of a squared binomial:
$color(white)("XXXX")$ $color(white)("XXXX")$ $(x+a)^2 = x^2+2ax+a^2$
$color(white)("XXXX")$ then the third term needs to be $(a^2) = (8/2)^2$
$x^2-8x+(8/2)^2 = -12 +(8/2)^2$

$x^2-8x+4^2 = -12 +16$

$color(white)("XXXX")$ rewrite the left side as a squared binomial
$color(white)("XXXX")$ and simplify the right side.
$(x-4)^2 = 4$

$color(white)("XXXX")$ Take the square root of both sides
$x-4 = +-2$

$color(white)("XXXX")$ Add 4 to both sides
$x=6$
or
$x=2$

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How do you solve the quadratic equation by completing the square: $x^2 – 8x + 12 = 0$ ?

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How do you solve the quadratic equation by completing the square: x^2 – 8x + 12 = 0x^2 – 8x + 12 = 0?

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How do you solve the quadratic equation by completing the square: $x^2 – 8x + 12 = 0$ ?