Question

X square + 17 X + 66 =0
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Answer 1

Answer:

x = -6                                OR                  x = -11

Step-by-step explanation:

Given Equation:

$x^{2} + 17x + 66 = 0$

Here, you have to split the middle term of the equation, i.e., 17x, into 2 numbers in such a way that the product of those 2 numbers equals to the product of the first and the third term of the above equation, and the sum of those 2 numbers should also be equal to the sum of the original middle term.

So, after applying it, we get the 2 terms as:

+11 and +6

Now, the new equation will be

$x^{2} + 6x + 11x + 66$

Now, find out the common factor between the first 2 terms of the new equation, and then proceed to find out the common factor between the next 2 terms.

In the first 2 terms, the common factor is x.

In the 3rd and the 4th terms, the common factor is 11.

Now, we will get

x(x + 6) + 11(x + 6) = 0

Now, there are 2 terms to the equation, as underlined and made bold above.

Take out the common factor between the 2 terms, i.e., (x + 6).

We will then get

(x + 6)(x + 11) = 0

Now, we must take each bracket and equate it to zero.

This means that

x + 6 = 0                          OR                   x + 11 = 0

After normal simplification, we will get

x = -6                                OR                  x = -11