Answer:
x = -8/3 = -2.667
x = -7/3 = -2.333
Step-by-step explanation:
Equation at the end of step 1 :
(((3x + 5)2) + 5 • (3x + 5)) + 6 = 0
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 9x2+45x+56
The first term is, 9x2 its coefficient is 9 .
The middle term is, +45x its coefficient is 45 .
The last term, "the constant", is +56
Step-1 : Multiply the coefficient of the first term by the constant 9 • 56 = 504
Step-2 : Find two factors of 504 whose sum equals the coefficient of the middle term, which is 45 .
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 21 and 24
9x2 + 21x + 24x + 56
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (3x+7)
Add up the last 2 terms, pulling out common factors :
8 • (3x+7)
Step-5 : Add up the four terms of step 4 :
(3x+8) • (3x+7)
Which is the desired factorization
Solve : 3x+7 = 0
Subtract 7 from both sides of the equation :
3x = -7
Divide both sides of the equation by 3:
x = -7/3 = -2.333
Solving a Single Variable Equation :
3.3 Solve : 3x+8 = 0
Subtract 8 from both sides of the equation :
3x = -8
Divide both sides of the equation by 3:
x = -8/3 = -2.667
Supplement : Solving Quadratic Equation Directly
Solving 9x2+45x+56 = 0 directly
