Final answer:
The solutions to the quadratic equation x²+6x-6=10 are x=2 and x=-8, found by rearranging the equation and applying the quadratic formula.
Step-by-step explanation:
The equation provided by the student, x²+6x-6=10, is a quadratic equation, which we can solve by first bringing it into standard form. We'll achieve this by moving all terms to one side to get 0 on the other side, resulting in x²+6x-16=0. Next, we apply the quadratic formula, x = (-b ± √(b²-4ac)) / (2a), where a=1, b=6, and c=-16. Substituting these values into the formula gives us the solutions for x.
First, calculate the discriminant √(6²-4(1)(-16))=√(36+64)=√100, which simplifies to 10. The solutions are then x = (-6 ± 10) / 2. So there are two solutions: x = (4 / 2) = 2 and x = (-16 / 2) = -8.