Solve equation by the method of your choice?

Question

(x - 10)(x - 2) = -20

Answer 1

x^2-12x+20=-20
x^2-12x+40=0
x=12+/-rt(144-160)/2
=6+/-2i

Answer 2

Step1. Simplified
(x-10)(x-2)=-20
x*2-2x-10x+20=-20
x*2-12x+20=-20
Step2 Set the equation to zero
At this point ask your self what makes this equation equal to zero
Ans. if you add both side +20
x*2-12x+20+20=-20+20
x*2-12x+40=0 Equation
Step3. Solve for x
x*2-12x+40=0
(x-8)(x-5)=0 x=8, x=5 will make this equation equal to zero
Many people and my self has hard time to simplifying the equation. Then
How to do it.
I don't have a specific answer.
But the way I do it is to call (-12x ) the inner and the (+40 )the outer. Knowing that I ask my self, which 2 numbers multiplied will give me (+40), and at the same time if I add or subtract them will give me( -12). In this case was easy 8 multiplied 5. The importance is the sign +or -. Now let see if works, you have 8 and 5 if you add them together will make (+12 ) but you need (-12). Next question that you ask your self is that if I make them (-8) and (-5), and you add them together will give you (-12) Ans. yes. But at the same time if you multiply them will give you (+40)Ans. yes Solved Problem


Step4. Check your ans. by plugging the 8 then 5 to the equation and should give you 0=0 if not it is a mistake sum where

Answer 3

Open the equation first.

x^2 - 12x + 20 = -20

Set it equal to 0

x^2 - 12x + 20 + 20 = -20 + 20
x^2 - 12x + 40 = 0

Factor it again. Nothing leapt to mind, so I went for the formula to find the roots of a quadratic equation. (-b +/- sqr(b^2 - 4ac))/2a

x = (-12 +/- sqr(144 - 160)/2
x = (-12 +/- sqr(-16))/2

x = -6 + 2i and -6 - 2i

Reality is that if you solve this equation repeatedly, it forms a parabola with the lowest point at x = 6 and y = -16.

Answer 4

x^2-12x+20=-20
x^2-12x+40=0
x^2-12x=36=-4
(x-6)^2=-4
x-6=+-2i
x=6+-2i