# yet another completing the square problem !!?

3x^2-9x=0

complete the square.

explain & list out steps please.

Relevance
• Anonymous

Same process as the last one. To complete a square:

 Divide the equation by the coefficient of the x² term.

 "Half going down, square going up."

 Take the square root of both sides and solve for x.

3x² - 9x = 0 [Divide everything by 3.]

x² - 3x = 0 [Rewrite with blanks, then fill them in. "Half going down, square going up."]

x² - 3x + ___ = 0 + ___

(x + ___)² = 0 + ___

Half of -3 is -3/2. This goes on the blank inside the parentheses.

(-3/2)² = 9/4. This goes on the blank above the parentheses (and to the ones on the right side of the equation). Now solve for x.

x² - 3x + 9/4 = 0 + 9/4

(x - 3/2)² = 9/4

√(x - 3/2)² = √(9/4)

|x - 3/2| = 3/2

x - 3/2 = ±3/2

x = 3/2 ± 3/2

x = 6/2 = 3 or x = 0/2 = 0.

x = 3 or x = 0.

• Anonymous

1) Divide out a "3":

3(x^2 - 3x) = 0

2) Take the "-3x" term and divide the coefficient by 2

-3 / 2 = -3/2

3) Find the square of -3/2

(-3/2)^2 = 9/4

4) You've found the number to add to (x^2 - 3x) to get a perfect square trinomial, so add it to the terms:

3(x^2 - 3x + 9/4)

5) Since you've added it to one side of the equation, add it to the other. But, since it is in the parentheses, multiply it by the "3" outside of the parentheses first:

3(x^2 - 3x + 9/4) = 3*9/4

6) Write the trinomial as the square of a binomial:

3 (x - (3/2))^2 = 27/4

(x - (3/2))^2 = 9/4

7)Take square roots of each side and solve(remember if you take a square root, the answer is either negative or positive):

x - (3/2) = +/-3/2

x = 0 or 3

• To complete the square of the equation 3x^2 - 9x = 0

or it is x^2 - 3x = 0

You have to take the coefficient of x and divide by 2 and square and add and substract this number, you will complete the square.

In this example, the coefficient of x is 3 and divide by 2 it becomes 3/2 and by squaring you get 9/4

Now, x^2 - 3x = 0, becomes x^2 - 3x + 9/4 = 9/4

or (x - 3/2)^2 = 9/4

• 3x^2 - 9x = 0

divide everything by 3

x^2 - 3x = 0

find half of 3, square it, add to both sides

x^2 - 3x + (9/4) = (9/4)

factor left side into a perfect square

(x - (3/2))^2 = (9/4)

sqrt both sides

x - (3/2) = ±(3/2)

x = (3/2) ± (3/2)

x = 0 or (6/2)

x = 0 or 3

ANS : 0 or 3

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• 3x^2 - 9x = 0

3x^2 = 9X

X^2 = 3x

x^2 - 3x = 0

x (x - 3) = 0

x = 0, or x = 3

You can double check the answers by plugging each value of X back into your original equation.