Question

FAN AND MEDAL
simplify the expression
(x - 5)(x - 5) = 144
PLEASE HELP ASAP

Answer 1

simplify the left hand side

(x - 5)(x - 5)
= x(x - 5) -5(x - 5)
=

Answer 2

i have no idea whats next

Answer 3

@UnkleRhaukus

Answer 4

expand

x(x - 5)

Answer 5

x^2 - 5x?

Answer 6

yes
now do the same with 5(x-5)

Answer 7

so x^2 - 5x*x^2 - 5x

Answer 8

@leon549

Answer 9

not quite, what did you got when expanding
5(x-5)

Answer 10

5x - 25?

Answer 11

yeah, so you have

(x - 5)(x - 5)
= x(x - 5) -5(x - 5)
= x^2 - 5x - (5x - 25)
=

Answer 12

(x - 5)(x - 5) = x(x - 5) -5(x - 5)
= x^2 - 5x - (5x - 25)
=x^2 - 5x-5x +5

Answer 13

60
leon549
Medals 0

(x - 5)(x - 5) = x(x - 5) -5(x - 5)
= x^2 - 5x - (5x - 25)
=x^2 - 5x-5x +25

Answer 14

im very lost and i have three minutes to finish my quiz could someone explain like the whole thing in one message?? then ill do my two other problems of the same thing myself

Answer 15

how do you simplify it past what you guys have already done? @leon549 @UnkleRhaukus

Answer 16

combine the x terms

Answer 17

then you have

x^2 -10x +25 = 144

Answer 18

okay so should we subtract 25?

Answer 19

yeah, subtract 25 from both sides

Answer 20

so x^2 - 10x = 119

Answer 21

then subtract 119 from both sides

Answer 22

so x^2 - 10x - 119 = 0?

Answer 23

you have a quadratic

(x+ a )(x+ b) = 0

a * b = -119

a+b = -10

Answer 24

or use quadratic formula

Answer 25

so what do i do now? sorry im so out of it i was absent for a few days

Answer 26

@UnkleRhaukus

Answer 27

do you want to use the quadratic formula?

Answer 28

i dont know how so whatevers easiest

Answer 29

For a quadratic equation
\[ax^2+bx+c=0\]
the quadratic formula is
\[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]

Answer 30

so how do i put my equation into that?

Answer 31

you have
\[x^2 - 10x - 119 = 0\]
so
\(a=1\), \(b=-10\), \(c=-199\)

\[x=\frac{-(-10)\pm\sqrt{(-10)^2-4(1)(-119)}}{2(1)}\\\quad=\]

Answer 32

(it turns out ok, i promise)

Answer 33

so x = -7 or 17?

Answer 34

yes!

Answer 35

thank you so much for working with me on this!!

Answer 36

if we knew our 17 times tables we might have gotten

(x+7)(x-17) = 0

which has the same solutions

as (x+7) = 0 => x = -7
or (x-17) = 0 => x = 17

Answer 37

this question is not "simplify" it is "solve for x"

Answer 38

x = ... , is as simple as it gets.

Answer 39

\[(x-5)^2=144
\\x-5=12\iff x=14\\
x-5=-12\iff x=-7\]

Answer 40

ok actually \(x-5=12\iff x=17\)

Answer 41

oh, shortcut.

Answer 42

nice.

Answer 43

takes two steps only and "simplify" has nothing to do with it
no, it is not a shortcut, it is how you solve a quadratic equation

Answer 44

thank you though! \(\color\magenta\heartsuit\)