Question

Fan&Medal!!!!

Solve for x
x2 - 3|x - 2| - 4x = - 6

Answer 1

start by isolating |x-2| to the left hand side

Answer 2

@Chris01 are you still here?

Answer 3

yes

Answer 4

can you bring |x-2| to one side, and all the other terms to the other side?

Answer 5

sorry i'm confused I don't know how to do that part

Answer 6

ok

Answer 7

x^2 - 3|x - 2| - 4x = - 6

let's first subtract x^2 from both sides

so we'll have

x^2 - x^2 -3| x-2| -4x = -6 -x^2

=

-3| x-2| -4x = -6 -x^2

Answer 8

then we add 4x to both sides to cancel out the -4x as well so we get

-3| x-2| = -6 -x^2 +4x

Answer 9

now we divide both sides by -3

Answer 10

| x-2| = (-6 -x^2 +4x) / -3

\[\left| x-2 \right| = 2*\frac{ x^2 }{ 3 }-\frac{ 4x }{ 3 }\]

Answer 11

now, once we finally have |x-2| isolated we can eliminate the absolute stripes.

we do this by making two versions of the equation, one positive and one negative

Answer 12

\( \Large \left| x-2 \right| = 2+\frac{ x^2 }{ 3 }-\frac{ 4x }{ 3 } \)

becomes

\( \Large x-2 = 2+\frac{ x^2 }{ 3 }-\frac{ 4x }{ 3 } \) and \( \Large x-2 =- 2-\frac{ x^2 }{ 3 }+\frac{ 4x }{ 3 } \)

Answer 13

now we solve both of these for x

Answer 14

starting with \( \Large x-2 = 2+\frac{ x^2 }{ 3 }-\frac{ 4x }{ 3 }\)

probably best to multiply both sides by 3 to get rid of fractions

\( \Large 3x-6 = 6+x^2-4x\)

now get everything to one side

\( \Large 0 = 6+x^2-4x-3x+6\)

simplify

\( \Large x^2-7x+12=0\)

factorize

\( \Large (x-4)(x-3)=0\)

x=3 or x=4

that's already two of the 4 solutions

if you solve the other part you get the other two solutions

Answer 15

thanks man!!

Answer 16

yw

Answer 17

to clarify, the other two solutions are in \(\Large x-2 =- 2-\frac{ x^2 }{ 3 }+\frac{ 4x }{ 3 }\) (the 'negative' part of the equation)