Question

What are the roots of the equation?

x^2+24=−11x

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Answer 1

`x_1 = -8`

`x_2 = -3`

Explanation:

Given the equation:

`x^2+24 = -11x`

Add 11x to both sides we have;

`x^2+11x+24 = 0`

Split the middle terms we have;

⇒
`x^2+8x+3x+24 = 0`

⇒
`x(x+8)+3(x+8)= 0`

⇒
`(x+8)(x+3)= 0`

By zero product property we have;

x+8 = 0 and x+3= 0

⇒x = -8 and x = -3

Therefore, the roots of the given equations are:

`x_1 = -8`

`x_2 = -3`

Answer 2

The correct answers are:

x=-3 and x=-8.

Explanation:

We can first write this in standard form, ax²+bx+c=0. To do this, we will add 11x to both sides:
x²+24+11x=-11x+11x
x²+11x+24=0.

Now we can factor this. Look for factors of c, 24, that sum to b, 11. Factors of 24 are:
1 and 24 (sum 25)
2 and 12 (sum 14)
3 and 8 (sum 11)
4 and 6 (sum 10).

The factors we need are 3 and 8, since they sum to 11. This gives us factored form:
(x+3)(x+8)=0.

Using the zero product property, we know that in order to have a product of 0, one or both of the factors must be 0. This means we have:
x+3=0 or x+8=0.

Solving the first equation:
x+3-3=0-3
x=-3.

Solving the second equation:
x+8-8=0-8
x=-8.