Question

How do you solve `(x - \frac { 1} { 3} ) ^ { 2} + 2( x - \frac { 1} { 3} ) ( x + \frac { 1} { 3} ) + ( x + \frac { 1} { 3} ) ^ { 2} = ( 2x + 1) ^ { 2}`?

Answer 1

`x=-1/4`

Explanation:

You have to expand all the brackets first:

`color(blue)((x-1/3)^2) + color(red)(2(x-1/3)(x+1/3)) + color(purple)((x+1/3)^2) = color(lime)((2x+1)^2)`

`color(blue)(x^2 -(2x)/3 +1/9) + color(red)(2(x^2 -1/9)) +color(purple) (x^2 +(2x)/3 +1/9) = color(lime)(4x^2 +4x+1)`

There are many additive inverses which add to `0`

`color(blue)(cancelx^2 cancel(-(2x)/3) +1/9) + color(red)(cancel(2x^2) -2/9) +color(purple)(cancelx^2 +cancel((2x)/3) +1/9) = color(lime)(cancel4x^2 +4x+1)`

Simplify:

`cancel(2/9)-cancel(2/9) = 4x+1`

Solve for `x`

`0-1=4x`

`-1/4 =x`