Solve by completing the square?

Question

x^2 - 18x +80 = 0

Answer 1

x^2 - 18x +80 = 0

you can slove it with 2 ways
first;
x^2 - 18x +80 = 0
Delta = b^2 - 4ac => (-18)^2 - 4*1*80 =324 - 320 = 4
Delta = 4

x1 = (-b + √Delta)/2a => [-(-18) + √4]/2 = 18+2/2 = 20/2 = 10

x2 = (-b - √Delta)/2a => [-(-18) + √4]/2 = 18- 2/2 = 16/2 = 8


Second
you should find 2 numbers that when you add them together the result would be -18
and when you multiply them together the result would be +80

it means u need this function
(x + a )(x + b ) so u need to find a and b.
and ; a= - 10 ; b= -8
a+b= -10 + (-8) = -10-8= -18
a*b = -10 * (-8) = + 80
so u have this now
(x + a )(x + b) = (x -10 ) (x -8) =0
(x -10 )=0 .....> x=10
(x -8) =0 .....> x=8

Answer 2

x^2 - 18x + 80 = 0

Subtract 80 from each side:

x^2 - 18x = - 80

what number multiplied by "2" equals "-18"
"-9 " works. Now, sqaure "-9"
You get 81
Add this to each side:

x^2 - 18x + 81 = - 80 + 81

The left side is now a perfect square(square it out, it works)

(x - 9)^2 = 1

Take square roots of each side:

x - 9 = 1
x = 10


Check by plugging in:

(10)^2 - 18(10) + 80 = 0
100 - 180 + 80 = 0
0 = 0

x = 10 works

Answer 3

x^2 - 18x +80 = 0

x^2 - 18x +81 -1 = 0. Complete the square by dividing the 'x' coefficient (-18) by 2 and squaring it to get 81. Change +80 to +81 -1.

(x-9)*(x-9) -1 = 0. Since (x-9) squared is equal to x^2 - 18x +81. (You can verify this using FOIL)

(x-9)^2 = 1

(x-9) = +/-1. Take square root of each side

x=10, x=8

Answer 4

x^2 - 18x + 80 = 0
x^2 - 18x = -80
x^2 - 18x + 81 = 1
(x - 9)^2 = 1
x - 9 = +1 or -1
x = 10 or 8

ANS : 8 or 10

Answer 5

First you have to factor the equation. Find two numbers that multiply to get 80 and add to get -18. That would be -10 and -8.
So, (x-8)(x-10) = 0 Then you set each factor equal to zero and solve.
x-8=0
so x=8
x-10=0
so x=10
Your two answers are 8 and 10.

Answer 6

x^2-2*9x+9^2-9^2+80=0
(x-9)^2-81+80=0
(x-9)^2=1
(x-9)=±√1
hence, x=9±1=10,8

Answer 7

If you put 5% of the effort you waste in posting questions here on studying and doing your homework yourself. You'll learn and will still have time to relax or play.