Question

For5, use the square root method to solve the quadratics.
5) 7 - 3x2 = -20

Answer 1

`\mathbf{Task.} ~ \mathrm{For~5,~use~the~square~root~method~to~solve~the~quadratics.}`

`5) ~ 7 - 3x^(2) = -20;`

`\mathrm{Subtract~7~from~both~sides~of~the~equation.}`

`7 - 3x^(2) - 7= -20 - 7;`

`\mathrm{Let's~calculate~the~difference.}`

`{-3x^(2)} = -27;`

`\mathrm{Divide~both~sides~of~the~equation~by~}{-3}.`

`\frac{{-3x^(2)} }{-3} = (-27)/(-3) ;`

`\mathrm{Find~the~quotient.}`

`x^(2) = 9;`

`\mathrm{Extract~the~arithmetic~square~ root~of~both~sides~of~the~equation.}`

`\sqrt{x^(2)} = √(9);`

`\mathrm{Use~the~rule\colon} \sqrt{a^(2)} = |a|.`

`|x| = 3;`

`\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.`

`\displaystyle \left [ {{x_(1) = -3,} \atop {x_(2) = 3. ~~}} \right.`

`Answer\colon ~{-3}; ~ 3. ~ \blacktriangle`