hello,if you have an equation like
(x-2)^2 +(2x-3) ^2= (3x-7) ^2
is there any way to find the value of x?
thanks
Hello, shuping!
Yes, multiply it out . . .If you have an equation like: $\displaystyle (x-2)^2 +(2x-3) ^2 \:= \3x-7) ^2$
is there any way to find the value of $\displaystyle x$ ?
We have: .$\displaystyle x^2 - 4x + 4 + 4x^2 - 12x + 9 \;= \;9x^2 - 42x + 49$
. . which simplifies to: .$\displaystyle 4x^2 - 26x + 36 \;= \;0\quad\Rightarrow\quad 2x^2 - 13x + 18 \;= \;0$
. . which factors: .$\displaystyle (x - 2)(2x - 9) \;= \;0$
. . and has roots: .$\displaystyle \boxed{x\:=\:2,\;\frac{9}{2}}$