Question

choose an action to perform.$7y^{2}+11y - 6=0$ways to rewrite expressions|action|corresponding tasks|| ---- | ---- ||factor expression|combine like terms||distribute|evaluate numerical||rewrite in different forms|factor quadratic||rewrite using operations|rewrite fractions||rewrite signs||equation transformations|action| || ---- | ---- ||add to both sides|||subtract from both sides|||multiply both sides|||divide both sides|||apply quadratic formula||other actions|action| || ---- | ---- ||apply zero product property|||isolate roots||

Explanation:

Step1: Identify quadratic coefficients

For $ay^2+by+c=0$, $a=7$, $b=11$, $c=-6$

Step2: Apply quadratic formula

Quadratic formula: $y=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute values:
$y=\frac{-11\pm\sqrt{11^2-4(7)(-6)}}{2(7)}$

Step3: Calculate discriminant

$\sqrt{121 + 168}=\sqrt{289}=17$

Step4: Solve for two y-values

First solution: $y=\frac{-11+17}{14}=\frac{6}{14}=\frac{3}{7}$
Second solution: $y=\frac{-11-17}{14}=\frac{-28}{14}=-2$

Answer:

$y=-2$ and $y=\frac{3}{7}$