Question

If someone could help with a few that would be amazing! even just the first step!

Answer 1

`\sf\\1.\ x^2-100=0\\or,\ x^2-10^2=0\\or,\ (x+10)(x-10)=0\\\therefore\ x=\pm10`

`\sf\\2.\ 25x^2=4\\or,\ 25x^2-4=0\\or,\ (5x)^2-2^2=0\\or,\ (5x+2)(5x-2)=0\\or,\ x=-2/5,\ 2/5\\\therefore\ x=\pm2/5`

`\sf\\3.\ 5x^2-11=234\\or,\ 5x^2=234+11=245\\or,\ x^2=245/5=49\\or,\ x^2-49=0\\or,\ x^2-7^2=0\\or,\ (x+7)(x-7)=0\\\therefore\ x=\pm7`

`\sf\\4.\ (1)/(3)x^2+14=26\\\\or,\ (1)/(3)x^2=12\\\\or,\ x^2=12(3)=36\\or,\ x^2-36=0\\or,\ x^2-6^2=0\\or,\ (x+6)(x-6)=0\\\therefore\ x=\pm6`

`\sf\\5.\ 2x^2-3=-3\\or,\ 2x^2=3-3=0\\or,\ x^2=0\\\therefore\ x=0`

`\sf\\6.\ 9x^2-1=63\\or,\ 9x^2=63+1=64\\or,\ 9x^2-64=0\\or,\ (3x)^2-8^2=0\\or,\ (3x+8)(3x-8)=0\\or,\ x=-3/8,\ 3/8\\\therefore\ x=\pm3/8`

`\sf\\7.\ x^2-1=39\\or,\ x^2=40\\or,\ x=\pm√(40)\\or,\ x=\pm√(4*10)\\or,\ x=\pm√(2^2*10)\\or,\ x=\pm2√(10)`

`\sf\\8.\ 5x^2=90\\or,\ x^2=90/5=18\\or,\ x^2=2*9\\or,\ x^2=2*3^2\\or,\ x=\pm√(2*3^2)\\or,\ x=\pm3\sqrt2`

`\sf\\9.\ 4x^2-20=22\\or,\ 4x^2=22+20=42\\or,\ x^2=42/4=21/2\\\therefore\ x=\pm\sqrt{(21)/(2)}`

`\sf\\10.\ 3x^2+4=166\\or,\ 3x^2=162\\or,\ x^2=162/3=54\\or,\ x^2=9*6=3^2*6\\or,\ x=\pm√(3^2*6)\\or,\ x=\pm3\sqrt6`

You may solve all of these questions like 7-10 were solved, without using a² - b² formulae. Hope this helps!