# Thread: algebra problem

1. ## algebra problem

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

2. Hello, shuping!

If you have an equation like: $(x-2)^2 +(2x-3) ^2 \:= \3x-7) ^2" alt="(x-2)^2 +(2x-3) ^2 \:= \3x-7) ^2" />

is there any way to find the value of $x$ ?
Yes, multiply it out . . .

We have: . $x^2 - 4x + 4 + 4x^2 - 12x + 9 \;= \;9x^2 - 42x + 49$

. . which simplifies to: . $4x^2 - 26x + 36 \;= \;0\quad\Rightarrow\quad 2x^2 - 13x + 18 \;= \;0$

. . which factors: . $(x - 2)(2x - 9) \;= \;0$

. . and has roots: . $\boxed{x\:=\:2,\;\frac{9}{2}}$