H. 3 (5x – 2) + 30% of x = 60
Answers
Answer:
STEP
1
:
Equation at the end of step 1
((30 • (x3)) - 5x2) - 60x
STEP
2
:
Equation at the end of step
2
:
((2•3•5x3) - 5x2) - 60x
STEP
3
:
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
30x3 - 5x2 - 60x = 5x • (6x2 - x - 12)
Trying to factor by splitting the middle term
4.2 Factoring 6x2 - x - 12
The first term is, 6x2 its coefficient is 6 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -12
Step-1 : Multiply the coefficient of the first term by the constant 6 • -12 = -72
Step-2 : Find two factors of -72 whose sum equals the coefficient of the middle term, which is -1 .
-72 + 1 = -71
-36 + 2 = -34
-24 + 3 = -21
-18 + 4 = -14
-12 + 6 = -6
-9 + 8 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 8
6x2 - 9x + 8x - 12
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (2x-3)
Add up the last 2 terms, pulling out common factors :
4 • (2x-3)
Step-5 : Add up the four terms of step 4 :
(3x+4) • (2x-3)
Which is the desired factorization
Final result :
5x • (2x - 3) • (3x + 4)
3 (5x – 2) + 30% of x = 60
15x - 6 + 30/100 × x = 60
15x - 6 + 3/10 × x = 60
15x -60+3/10 × x = 60
15x -57/10 × x = 60
15x -57x/10 = 60
150x-57x/10 = 60
150x-57x = 600
93x = 600
x = 600/93