Final answer:
To solve the equation x²-16=-2x-1, we rearrange it to x²+2x-15=0, factor it to (x+5)(x-3)=0, and find the solutions x=-5 and x=3.
Step-by-step explanation:
The student has been asked to solve the equation x²-16=-2x-1 by factoring. To do this, first, we need to rearrange the equation to have all terms on one side, resulting in a standard quadratic form x²+2x-15=0. To factor the quadratic equation, we search for two numbers that multiply to -15 (the constant term) and add up to 2 (the coefficient of the x term). These numbers are 5 and -3. Thus, the equation factors as (x+5)(x-3)=0. To find the values of x, we set each factor equal to zero and solve for x, which gives us x=-5 or x=3.