Indicate the correct solution to the quadratic equation below or whether it has no solution. \( y^{2}-7 y=8 y+10 \) Select one: no solution \( x=10 \) and 1 -0.64 and 15.64 approximately \( x=5 \) and -2

To solve the equation \( y^2 - 7y - 8y - 10 = 0 \), first simplify it to \( y^2 - 15y - 10 = 0 \). Next, use the quadratic formula \( y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) where \( a=1, b=-15, c=-10 \). This results in the solutions \( y \approx 15.64 \) and \( y \approx -0.64 \). So the correct answer is approximately -0.64 and 15.64. Let's break it down! After combining like terms, you end up with a standard quadratic equation. When plugged into the quadratic formula, the resultant values might seem foreign at first, but take a moment to visualize them on a graph. The two points where your parabola intersects the x-axis represent the solutions to the equation. Always double-check your signs and calculations to avoid hiccups in the process!