Question

Tori and Gavin were trying to solve the equation:

(x+1) ^2 −3=13. Tori said, ""I'll add 3 to both sides of the equation and solve using square roots."" Gavin said, ""I'll multiply
(x+1)^2 and rewrite the equation as x^2 +2x+1−3=13. Then I'll subtract 13 from both sides, combine like terms, and solve using the quadratic formula with a=1, b=2, and c=−15."" Whose solution strategy would work?"
a. Tori's
b. Gavin's
c. Both would work
d. Neither would work

Answer 1

Both Tori's and Gavin's strategies for solving the equation (x+1)^2 − 3 = 13 are valid. Tori's method involves adding 3 and taking square roots, while Gavin's involves rewriting and using the quadratic formula.

Step-by-step explanation:

The equation that the student needs to solve is (x+1)^2 − 3 = 13. Both Tori's and Gavin's solution strategies would work to solve the equation, though they approach it differently.

Tori's method: Adding 3 to both sides results in (x+1)^2 = 16. Taking the square root of both sides gives us x + 1 = ±4, leading to two possible solutions for x.

Gavin's method: Multiplying (x+1)^2 and rewriting the equation as x^2 + 2x + 1 − 3 = 13, then combining like terms and subtracting 13 from both sides, results in x^2 + 2x - 15 = 0. This quadratic equation can indeed be solved using the quadratic formula with a = 1, b = 2, and c = -15 to find the values of x.

Thus, the correct answer is c. Both would work.