Question

What equation results from completing the square and then factoring?
x^2 - 10x = 46

Answer 1

`\bold{Hello!}\\\bold{Your~Answer~Is~Below!}`

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`\bold{Solution~Steps:}`

`1.)~Quadratic~equations~such~as~this~one~can~be~solved~by~completing\\~the~square.~In~order~to~complete~the~square,~the~equation~must~first~be~in~the~form:`

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  `\bold{x^2~\frac{+}}~bx=c}`

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  `\bold{x^2-10x=46}`

`2.)~Divide-10~by~2:`

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  `\bold{-10}` ÷
  `\bold{2=-5}`

`3.)~Add~the~square~of -5~to~both~sides~of~the~equation:`

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  `\bold{-5^2=25}`

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  `\bold{46+25=71}`

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  `\bold{This~step~makes~the~left~hand~side~of~the~equation~a~perfect~square.}`

`4.)~Factor~x^2-10x+25:`

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  `\bold{In~general,~when~x^2+bx+c~is~a~perfect~square,~it~can~be~factored~as~(x+(b)/(2)^2).}`

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  `\bold{(x-5)^2=71}`

`5.)~Take~the~square~root~of~both~sides:`

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  `\bold{√((x-5)^2)=√(71)}`

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  `\bold{x-5=√(71)}`

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  `\bold{x+5=√(71)}`

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`\bold{Answer:}`

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  `\bold{\frac{+}~√(71)}`

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  `\bold{x=5+√(71)}`

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  `\bold{x=5-√(71)}`

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`\bold{Hope~this~helps,}\\\bold{And~best~of~luck!}\\\\\bold{~~~~~~~-TotallyNotTrillex}`