X^2 - 12x + 19 in the form of (x + a)^2 + b ???

( x-6)^2 -17

Step-by-step explanation:

X^2 - 12x + 19

we need it in given below form

(x + a)^2 + b

we know that

lets convert that in same form

X^2 - 12x + 19 = x^2 + 2(-6)x + 19

comparing x^2 + 2(-6)x to x^2 + 2ax

we have a -6

now

(x-6)^2 = x^2 + 2(-6)x + 36

36 is missing in the x^2 + 2(-6)x + 19 hence to get that

we add and subtract 36 in the above equation

so we have

x^2 + 2(-6)x + 19 + 36 -36

rearranging  it \

(x^2 + 2(-6)x  + 36) -36 + 19    (x^2 + 2(-6)x  + 36 =( x-6)^2)

=>( x-6)^2 -17

comparing the above equation to

(x + a)^2 + b

we have a = -6

b = -17

( x-6)^2 -17

i dont know

step-by-step explanation:

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.