Answer:
1. x = 8
2. x = 2
Step-by-step explanation:
2 • (x - 5)2 - 18 = 0
2.1 Evaluate : (x-5)2 = x2-10x+25
3.1 Pull out like factors :
2x2 - 20x + 32 = 2 • (x2 - 10x + 16)
3.2 Factoring x2 - 10x + 16
The first term is, x2 its coefficient is 1 .
The middle term is, -10x its coefficient is -10 .
The last term, "the constant", is +16
Step-1 : Multiply the coefficient of the first term by the constant 1 • 16 = 16
Step-2 : Find two factors of 16 whose sum equals the coefficient of the middle term, which is -10 .
-16 + -1 = -17
-8 + -2 = -10 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and -2
x2 - 8x - 2x - 16
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-8)
Add up the last 2 terms, pulling out common factors :
2 • (x-8)
Step-5 : Add up the four terms of step 4 :
(x-2) • (x-8)
Which is the desired factorization
2 • (x - 2) • (x - 8) = 0
4.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
