Use the Quadratic Formula to solve for $y$ . $5 x ^ { 2 } + 10 x y + 11 y ^ { 2 } + 9 x - 10 y - 42 = 0$
A) $y = \frac { - ( 10 x - 10 ) \pm \sqrt { ( 10 x - 10 ) ^ { 2 } - 44 \left( 5 x ^ { 2 } - 9 x - 42 \right) } } { 22 }$
B) $y = \frac { ( 10 x - 10 ) \pm \sqrt { ( 10 x - 10 ) ^ { 2 } - 44 \left( 5 x ^ { 2 } + 9 x - 42 \right) } } { 22 }$
C) $y = \frac { - ( 10 x - 10 ) \pm \sqrt { ( 10 x - 10 ) ^ { 2 } - 44 \left( 5 x ^ { 2 } + 9 x - 42 \right) } } { 22 }$.
D) $y = \frac { - ( 10 x - 10 ) \pm \sqrt { ( 10 x - 10 ) ^ { 2 } - 44 \left( 5 x ^ { 2 } + 9 x - 42 \right) } } { 22 }$
E) $y = \frac { - ( 10 x - 10 ) \pm \sqrt { ( 10 x - 10 ) ^ { 2 } + 44 \left( 5 x ^ { 2 } + 9 x - 42 \right) } } { 22 }$

Question

Use the Quadratic Formula to solve for $y$ .​ $5 x ^ { 2 } + 10 x y + 11 y ^ { 2 } + 9 x - 10 y - 42 = 0$ ​
A) $y = \frac { - ( 10 x - 10 ) \pm \sqrt { ( 10 x - 10 ) ^ { 2 } - 44 \left( 5 x ^ { 2 } - 9 x - 42 \right) } } { 22 }$
B) $y = \frac { ( 10 x - 10 ) \pm \sqrt { ( 10 x - 10 ) ^ { 2 } - 44 \left( 5 x ^ { 2 } + 9 x - 42 \right) } } { 22 }$
C) $y = \frac { - ( 10 x - 10 ) \pm \sqrt { ( 10 x - 10 ) ^ { 2 } - 44 \left( 5 x ^ { 2 } + 9 x - 42 \right) } } { 22 }$.
D) $y = \frac { - ( 10 x - 10 ) \pm \sqrt { ( 10 x - 10 ) ^ { 2 } - 44 \left( 5 x ^ { 2 } + 9 x - 42 \right) } } { 22 }$
E) $y = \frac { - ( 10 x - 10 ) \pm \sqrt { ( 10 x - 10 ) ^ { 2 } + 44 \left( 5 x ^ { 2 } + 9 x - 42 \right) } } { 22 }$

Quizplus · Accepted Answer

The quadratic formula for $y$ is derived by treating the equation as a quadratic in $y$, where $a = 11$, $b = 10x - 10$, and $c = 5x^2 + 9x - 42$. The correct formula is $y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, which matches option C.

Use the Quadratic Formula to Solve For yyy ​ 5x2+10xy+11y2+9x−10y−42=05 x ^ { 2 } + 10 x y + 11 y ^ { 2 } + 9 x - 10 y - 42 = 05x2+10xy+11y2+9x−10y−42=0

Use the Quadratic Formula to Solve For $y$ $5 x ^ { 2 } + 10 x y + 11 y ^ { 2 } + 9 x - 10 y - 42 = 0$