Question

error analysis on a recent homework assignment, eli needed to solve this equation completely. he incorrectly wrote \g = -7\. solve the equation. what error did eli make?
( g^2 = 49 )
( g = square )
(simplify your answer. type an exact answer, using radicals as needed. use a comma to separate answers as needed.)
what error did eli make?
a. he did not square 49 correctly since ( 49^2
eq -7 ).
b. he did not solve the equation completely since there is a positive answer as well.
c. he did not take the square root of 49 correctly since ( (-7)^2
eq 49 ).
d. he did not solve the equation completely since there are two negative answers.

Explanation:

Step1: Isolate variable via square root

Take square root of both sides:
$$g = \pm\sqrt{49}$$

Step2: Simplify the square root

Calculate $\sqrt{49}$:
$$g = \pm7$$

Eli only provided one of the two solutions to the quadratic equation. A squared variable set equal to a positive number has both a positive and negative square root solution.

Answer:

$g = 7, -7$