Answer:
The answers to your questions are given below.
Step-by-step explanation:
x² – 24 = 10x
Using the format given in the question above, we shall determine the value of x as follow:
I. Make the equation equal to zero
x² – 24 = 10x
Rearrange
x² – 10x – 24 = 0
II. Find two numbers that multiply to __ and add to ___
Multiply the first term (i.e x²) and the last term (i.e –24). The result is –24x².
Find two factors of –24x² such that their sum will result to the 2nd term (i.e –10x). The numbers are 2x and –12x
Thus, Find two numbers that multiply to –24x² and add to –10x
III. Factored equation
x² – 10x – 24 = 0
x² + 2x – 12x – 24 = 0
x(x + 2) – 12(x + 2) = 0
(x – 12)(x + 2) = 0
Thus, the factored equation is:
(x – 12)(x + 2) = 0
IV. The solution are:
(x – 12)(x + 2) = 0
x – 12 = 0 or x + 2 = 0
x = 12 or x = –2
Thus, the solutions are x = 12 or x = –2
