Step-1 : Multiply the coefficient of the first term by the constant 36 • 1 = 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
36n2 - 6n - 6n - 1
Step-4 : Add up the first 2 terms, pulling out like factors :
6n • (6n-1)
Add up the last 2 terms, pulling out common factors :
1 • (6n-1)
Step-5 : Add up the four terms of step 4 :
(6n-1) • (6n-1)
Which is the desired factorization
Multiply (6n-1) by (6n-1)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (6n-1) and the exponents are :
1 , as (6n-1) is the same number as (6n-1)1
and 1 , as (6n-1) is the same number as (6n-1)1
The product is therefore, (6n-1)(1+1) = (6n-1)2
Equation at the end of step
2
:
(6n - 1)2 = 0
STEP
3
:
Solving a Single Variable Equation:
3.1 Solve : (6n-1)2 = 0
(6n-1) 2 represents, in effect, a product of 2 terms which is equal to zero
For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means : 6n-1 = 0
Add 1 to both sides of the equation :
6n = 1
Divide both sides of the equation by 6:
n = 1/6 = 0.167
Supplement : Solving Quadratic Equation Directly
Solving 36n2-12n+1 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
Answers & Comments
Answer:
n=1/6=0.167
The first term is, 36n2 its coefficient is 36 .
The middle term is, -12n its coefficient is -12 .
The last term, "the constant", is +1
Step-1 : Multiply the coefficient of the first term by the constant 36 • 1 = 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
36n2 - 6n - 6n - 1
Step-4 : Add up the first 2 terms, pulling out like factors :
6n • (6n-1)
Add up the last 2 terms, pulling out common factors :
1 • (6n-1)
Step-5 : Add up the four terms of step 4 :
(6n-1) • (6n-1)
Which is the desired factorization
Multiply (6n-1) by (6n-1)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (6n-1) and the exponents are :
1 , as (6n-1) is the same number as (6n-1)1
and 1 , as (6n-1) is the same number as (6n-1)1
The product is therefore, (6n-1)(1+1) = (6n-1)2
Equation at the end of step
2
:
(6n - 1)2 = 0
STEP
3
:
Solving a Single Variable Equation:
3.1 Solve : (6n-1)2 = 0
(6n-1) 2 represents, in effect, a product of 2 terms which is equal to zero
For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means : 6n-1 = 0
Add 1 to both sides of the equation :
6n = 1
Divide both sides of the equation by 6:
n = 1/6 = 0.167
Supplement : Solving Quadratic Equation Directly
Solving 36n2-12n+1 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
Parabola, Finding the Vertex:
4.1 Find the Vertex of y = 36n2-12n+1
Answer:
n=1/6=0.167
Step-by-step explanation:
((22•32n2) - 12n) + 1 = 0
2.1 Factoring 36n2-12n+1
The first term is, 36n2 its coefficient is 36 .
The middle term is, -12n its coefficient is -12 .
The last term, "the constant", is +1
Step-1 : Multiply the coefficient of the first term by the constant 36 • 1 = 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
36n2 - 6n - 6n - 1
Step-4 : Add up the first 2 terms, pulling out like factors :
6n • (6n-1)
Add up the last 2 terms, pulling out common factors :
1 • (6n-1)
Step-5 : Add up the four terms of step 4 :
(6n-1) • (6n-1)
Which is the desired factorization