solve- x^2-24x+144=0
Answers
Answer:
Factoring x2-24x+144
The first term is, x2 its coefficient is 1 .
The middle term is, -24x its coefficient is -24 .
The last term, "the constant", is +144
: Multiply the coefficient of the first term by the constant 1 • 144 = 144
: The two factors of 144 whose sum equals the coefficient of the middle term, which is -24 .
-144 + -1 = -145
-72 + -2 = -74
-48 + -3 = -51
-36 + -4 = -40
-24 + -6 = -30
-18 + -8 = -26
-16 + -9 = -25
-12 + -12 = -24
: the polynomial splitting the middle term using the two factors found above -12 and -12 .
x2 - 12x - 12x - 144
Add up the first 2 terms, like factors :
x • (x-12)
Add up the last 2 terms,
common factors :
12 • (x-12)
Add up the terms
(x-12) • (x-12)
the desired factorization
Multiplying Exponential Expressions :
1.2 Multiply (x-12) by (x-12)
To multiply exponential expressions which have the same base, add up their exponents.
the common base is (x-12) and the exponents are :
1 , as (x-12) is the same number as (x-12)1
and 1 , as (x-12) is the same number as (x-12)1
The product is therefore, (x-12)(1+1) = (x-12)2
(x - 12)2 = 0
Solving a Single Variable Equation :
: (x-12)2 = 0
(x-12) 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 : x-12 = 0
Add 12 to both sides of the equation :
x = 12
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