Question

Please help me what is the factored form of 7x^2-21x=0

Answer 1

The correct answer is 7x^2

Answer 2

First, divide by 7 so you have nothing in front.

$x^{2} -7=0$

Then we proceed with completing the square:

Normally we would move the constant to the right but in this case, there is none.

Take half of the x coefficient and square it. Add it to both sides.
So that's -3.
Half is $- \frac{3}{2}$.
Square it:
$( \frac{3}{2}) ^{2}= \frac{9}{4}$
Add it to both sides:

$x^{2} -3x + \frac{9}{4} = 0 + \frac{9}{4} \\ x^{2} -3x+ \frac{9}{4}= \frac{9}{4}$

Write the perfect square on the left:
$(x- \frac{3}{2} ) ^{2} = \frac{9}{4}$

Square root both sides:
$x- \frac{3}{2} = +/-\sqrt{ \frac{9}{4} }$

Solve for x:
$x= \frac{3}{2} +/- \sqrt{ \frac{9}{4} }$

Which simplifies to:
$x_{1} = 0 \\ x_{2} = 3$

Hope that helps.