Question

whats is the intermediate step in the form (x+a)^2=b as a result of completing the square for the following equatio? −6x^2+36x= −714

Answer 1

To complete the square for the equation we can first factor out the coefficient of x^2 to get:

-6(x^2 - 6x) = -714

Next, we need to add and subtract the square of half the coefficient of x, which is (6/2)^2 = 9. This will allow us to write the expression inside the parentheses as a perfect square:

-6(x^2 - 6x + 9 - 9) = -714

Now we can simplify the expression inside the parentheses by factoring it as a perfect square:

-6((x - 3)^2 - 9) = -714

Finally, we can simplify the expression on the left by distributing the -6:

-6(x - 3)^2 + 54 = -714

So the intermediate step in completing the square for the equation −6x^2+36x= −714 is -6(x - 3)^2 + 54 = -714.