Question

How do you solve `(2x+1)^2=(x+2)^2`?

Answer 1

`x=+-1`

Explanation:

`"expand factors on both sides using the FOIL method"`

`4x^2+4x+1=x^2+4x+4`

`"subtract " x^2" from both sides"`

`4x^2-x^2+4x+1=cancel(x^2)cancel(-x^2)+4x+4`

`rArr3x^2+4x+1=4x+4`

`"subtracting 4x from both sides, gives"`

`3x^2+1=4`

`"subtract 4 from both sides"`

`3x^2+1-4=4-4`

`rArr3x^2-3=0larrcolor(blue)" quadratic equation"`

`3(x^2-1)=0larrcolor(blue)" common factor of 3"`

`3(x-1)(x+1)=0larrcolor(blue)" difference of aquares"`

`"equate each factor to zero and solve"`

`x-1=0rArrx=1`

`x+1=0rArrx=-1`

`color(blue)"As a check"`

Substitute these values into the equation and if both sides are equal then they are the solutions.

`x=1to(2+1)^2=(1+2)^2to" True"`

`x=-1to(-1)^2=(1)^2to" True"`

`rArrx=+-1" are the solutions"`