I have installed JDK and JRE from this tutorial and have tried many methods of starting it up, yet my results are always the same. If any one could please help me I would be very grateful.

Exception in thread "Thread-3" java.lang.UnsatisfiedLinkError: /home/dennis/.minecraft/bin/natives/liblwjgl.so: /home/dennis/.minecraft/bin/natives/liblwjgl.so: wrong ELF class: ELFCLASS32 (Possible cause: architecture word width mismatch)
    at java.lang.ClassLoader$NativeLibrary.load(Native Method)
    at java.lang.ClassLoader.loadLibrary1(Unknown Source)
    at java.lang.ClassLoader.loadLibrary0(Unknown Source)
    at java.lang.ClassLoader.loadLibrary(Unknown Source)
    at java.lang.Runtime.load0(Unknown Source)
    at java.lang.System.load(Unknown Source)
    at org.lwjgl.Sys$1.run(Sys.java:69)
    at java.security.AccessController.doPrivileged(Native Method)
    at org.lwjgl.Sys.doLoadLibrary(Sys.java:65)
    at org.lwjgl.Sys.loadLibrary(Sys.java:81)
    at org.lwjgl.Sys.<clinit>(Sys.java:98)
    at net.minecraft.client.Minecraft.F(SourceFile:1853)
    at aoe.<init>(SourceFile:20)
    at net.minecraft.client.Minecraft.<init>(SourceFile:77)
    at anv.<init>(SourceFile:36)
    at net.minecraft.client.MinecraftApplet.init(SourceFile:36)
    at net.minecraft.Launcher.replace(Launcher.java:136)
    at net.minecraft.Launcher$1.run(Launcher.java:79)