Question

x^2+5x=0 solve by completing the square

Answer 1

First write x^2 + 5x = 0.

We focus on the left side first.

To get x^2 with FOIL, I need an x in both parentheses. So,
(x )(x )

To figure out what we need next, take the 5x term, and look at the 5. Then divide it by two, giving us 5/2.

So, (x 5/2)(x 5/2)

We have positive numbers so we will have to add.

Then, (x + 5/2)(x + 5/2).

When we FOIL we see, x^2 +5x + 25/4.

Our original equation was x^2 + 5x = 0.
So add 25/4 to both sides and get.
x^2 + 5x + 25/4 = 25/4.

But, we know that x^2 + 5x + 25/4 is just (x + 5/2)(x + 5/2) or (x + 5/2)^2.

So, (x + 5/2)^2 = 25/4.

Take the square root of both sides.

x + 5/2 = plus or minus 5/2.

So, x = 0 or x = -5.

Answer 2

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