Question

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

Answer 1

Answer:

x^2 - 10x = 46

Step-by-step explanation:

Answer 2

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

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 $\bold{Solution~Steps:}$

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

• $\bold{x^2~\frac{+}}~bx=c}$

• $\bold{x^2-10x=46}$

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

• $\bold{-10}$ ÷ $\bold{2=-5}$

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

• $\bold{-5^2=25}$

• $\bold{46+25=71}$

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

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

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

• $\bold{(x-5)^2=71}$

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

• $\bold{\sqrt{(x-5)^2}=\sqrt{71}}$

• $\bold{x-5=\sqrt{71}}$

• $\bold{x+5=\sqrt{71}}$

 

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 $\bold{Answer:}$

• $\bold{\frac{+}~\sqrt{71}}$

• $\bold{x=5+\sqrt{71}}$

• $\bold{x=5-\sqrt{71}}$

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