Solve for the specified variable. Assume that all other variables are nonzero
-$( b - 7 ) y ^ { 2 } - 11 y + 8 z = 0$; for $y$
A) $y = \frac { 11 \pm \sqrt { 121 + 32 b z - 224 z } } { b - 7 }$
B) $y = \frac { 11 \pm \sqrt { 121 - 32 b z + 224 z } } { 2 b - 14 }$
C) $y = \frac { 11 \pm \sqrt { 121 - 32 b z + 224 z } } { b - 7 }$
D) $y = \frac { 11 \pm \sqrt { 121 + 32 b z - 224 z } } { 2 b - 14 }$

Question

Quizplus · Accepted Answer

This equation is a quadratic equation in the form of $ay^2 + by + c = 0$, where $a = (b - 7)$, $b = -11$, and $c = 8z$. To solve for $y$, we use the quadratic formula $y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. Substituting the values of $a$, $b$, and $c$ into the formula gives $y = \frac{11 \pm \sqrt{(-11)^2 - 4(b-7)(8z)}}{2(b-7)}$, which simplifies to $y = \frac{11 \pm \sqrt{121 + 32bz - 224z}}{2b - 14}$, matching option D.

Solve for the Specified Variable (b−7)y2−11y+8z=0( b - 7 ) y ^ { 2 } - 11 y + 8 z = 0(b−7)y2−11y+8z=0

Solve for the Specified Variable $( b - 7 ) y ^ { 2 } - 11 y + 8 z = 0$