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Math Help - algebra problem

  1. #1
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    Exclamation 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
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, shuping!

    If you have an equation like: 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}}
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