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.