How do you solve using the completing the square method $9(x^2) - 18x = -3$ ?

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Answer 1 · 2018-04-10T18:41:44

You need to use the formula: $(a-b)^2=a^2-2ab+b^2$

If we manipulate the equation given to get $9x^2-18x+3=0$ , using the formula above we can see that:

$9x^2=a^2$ , and that $-18x=-2ab$

So from the first we have $3x=a$ and substituting this in the second we have

$-6 * 3x=-6a=-2ab$ , and then

$-6=-2b$ and from here $b=3$

Now completing the square in the equation given :

$9x^2-18x+3=9x^2-18x+9-6=0=(3x-3)^2-6=0$

that is:

$(3x-3)^2=6$ , and we have two solutions:

$(3x-3)=+sqrt6$
$(3x-3)=-sqrt6$ , and then:
$x=(3+sqrt6)/3$ and
$x=(3-sqrt6)/3$

How do you solve using the completing the square method 9(x^2) - 18x = -39(x^2) - 18x = -3?