Example2: Use the quadratic formula to solve the equation 4x²-9+12x
Answers
Answer:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
4*x^2+9-(12*x)=0
Step by step solution :
STEP
1
:
Equation at the end of step 1
(22x2 + 9) - 12x = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 4x2-12x+9
The first term is, 4x2 its coefficient is 4 .
The middle term is, -12x its coefficient is -12 .
The last term, "the constant", is +9
Step-1 : Multiply the coefficient of the first term by the constant 4 • 9 = 36
Step-2 : Find two factors of 36 whose sum equals the coefficient of the middle term, which is -12 .
-36 + -1 = -37
-18 + -2 = -20
-12 + -3 = -15
-9 + -4 = -13
-6 + -6 = -12 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and -6
4x2 - 6x - 6x - 9
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (2x-3)
Add up the last 2 terms, pulling out common factors :
3 • (2x-3)
Step-5 : Add up the four terms of step 4 :
(2x-3) • (2x-3)
Which is the desired factorization