Final answer:
The quadratic equation x²-2x-15=0 is solved using the quadratic formula, resulting in two solutions: x = 5 and x = -7.5.
Step-by-step explanation:
The student is attempting to solve a quadratic equation, specifically x²-2x-15=0, using the quadratic formula. To apply the quadratic formula, we must recognize the general form of a quadratic equation as ax²+bx+c=0, where 'a', 'b', and 'c' are coefficients. In our case, a=1, b=-2, and c=-15. The quadratic formula is given by x = (-b ± √(b²-4ac)) / (2a).
Substituting our coefficients into the formula provides us two solutions:
- x = (-(-2) ± √((-2)²-4(1)(-15))) / (2(1))
- x = (2 ± √(4+60)) / 2
- x = (2 ± √64) / 2
- x = (2 ± 8) / 2
- Our possible solutions for x are therefore 5 and -7.5.
Confirming this, we would get x = 5 and x = -7.5 as the solutions for the given quadratic equation, rounded to two decimal places as instructed.