determine x if 72 : 112 : : x : 28
Answers
Answer:
Step by Step Solution:
Step by step solution :STEP1:Equation at the end of step 1 (32x2 - 72x) - 112 = 0 STEP2:Trying to factor by splitting the middle term
2.1 Factoring 9x2-72x-112
The first term is, 9x2 its coefficient is 9 .
The middle term is, -72x its coefficient is -72 .
The last term, "the constant", is -112
Step-1 : Multiply the coefficient of the first term by the constant 9 • -112 = -1008
Step-2 : Find two factors of -1008 whose sum equals the coefficient of the middle term, which is -72 .
-1008 + 1 = -1007 -504 + 2 = -502 -336 + 3 = -333 -252 + 4 = -248 -168 + 6 = -162 -144 + 7 = -137 -126 + 8 = -118 -112 + 9 = -103 -84 + 12 = -72 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -84 and 12
9x2 - 84x + 12x - 112
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (3x-28)
Add up the last 2 terms, pulling out common factors :
4 • (3x-28)
Step-5 : Add up the four terms of step 4 :
(3x+4) • (3x-28)
Which is the desired factorization
Equation at the end of step2: (3x - 28) • (3x + 4) = 0 STEP3:Theory - Roots of a product
3.1 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.
Answer:
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