Use the Quadratic Formula to solve for y in the following equation. $36 x ^ { 2 } - 84 x y + 49 y ^ { 2 } - 70 x - 30 y = 0$
A) $\frac { - 42 x - 15 \pm \sqrt { - 84 x + 3655 } } { 49 }$
B) $\frac { 2 ( 42 x + 15 ) \pm \sqrt { - 84 x + 14620 } } { 49 }$
C) $\frac { 42 x + 15 \pm \sqrt { 4690 x + 225 } } { 49 }$
D) $\frac { 84 x + 30 \pm \sqrt { - 42 x + 7085 } } { 98 }$
E) $\frac { - 84 x - 30 \pm \sqrt { - 42 x + 4330 } } { 98 }$

Question

Quizplus · Accepted Answer

Using the quadratic formula, we get:

$$y=\frac{-(-84x)+\sqrt{(-84x)^2-4(36)(49y^2-70x-30y)}}{2(49)} 	ext{ or } y=\frac{-(-84x)-\sqrt{(-84x)^2-4(36)(49y^2-70x-30y)}}{2(49)}$$

Simplifying the expression inside the square root:

$$(-84x)^2-4(36)(49y^2-70x-30y)= 7056x^2-7056y^2+10080x+5040y$$

Now, we substitute this in the formula:

$$y=\frac{42x+15\pm\sqrt{(42x+15)^2-(7056x^2-7056y^2+10080x+5040y)}}{49}$$

After some simplification, we get:

$$y=\frac{42x+15\pm\sqrt{4690x+225}}{49}$$

Thus, the answer is C.

Use the Quadratic Formula to Solve for Y in the Following