MATH SOLVE

2 months ago

Q:
# What are the roots of the equation?x^2+24=−11xEnter your answers in the boxes.

Accepted Solution

A:

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.

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.