[tex]\mathbf{Task.} ~ \mathrm{For~5,~use~the~square~root~method~to~solve~the~quadratics.}[/tex]
[tex]5) ~ 7 - 3x^{2} = -20;[/tex]
[tex]\mathrm{Subtract~7~from~both~sides~of~the~equation.}[/tex]
[tex]7 - 3x^{2} - 7= -20 - 7;[/tex]
[tex]\mathrm{Let's~calculate~the~difference.}[/tex]
[tex]{-3x^{2}} = -27;[/tex]
[tex]\mathrm{Divide~both~sides~of~the~equation~by~}{-3}.[/tex]
[tex]\dfrac{{-3x^{2}} }{-3} = \dfrac{-27}{-3} ;[/tex]
[tex]\mathrm{Find~the~quotient.}[/tex]
[tex]x^{2} = 9;[/tex]
[tex]\mathrm{Extract~the~arithmetic~square~ root~of~both~sides~of~the~equation.}[/tex]
[tex]\sqrt{x^{2}} = \sqrt{9};[/tex]
[tex]\mathrm{Use~the~rule\colon} \sqrt{a^{2}} = |a|.[/tex]
[tex]|x| = 3;[/tex]
[tex]\mathrm{An~equation~of~the~form~} |f(x)|=a, \ a \geq 0, ~\mathrm{is~equivalent~to~a~union\colon} \displaystyle\left [ {{f(x)=-a,} \atop {f(x)=a.~~}} \right.[/tex]
[tex]\displaystyle \left [ {{x_{1} = -3,} \atop {x_{2} = 3. ~~}} \right.[/tex]
[tex]Answer\colon ~{-3}; ~ 3. ~ \blacktriangle[/tex]
