Josephine solved a quadratic equation: (x+6)^2=49. Her work is shown below.
Step 1: √(x+6)^2 = √49
Step 2: x+6 = 7
Step 3: x = 7−6
Step 4: x = 1
In which step did Josephine make an error?
A- step 4
B- step 1
C- step 2
D- step 3
Josephine made an error in Step 3.
The correct answer is D - step 3.
In step 3, Josephine incorrectly subtracted 6 from 7. The correct subtraction should have been x = 7 - 6, which would give x = 1. However, Josephine made a calculation mistake and wrote x = 7 - 6 instead, which is incorrect.
From Josephine's work, we can see that the given quadratic equation is (x+6)^2 = 49.
In step 1, Josephine correctly took the square root of both sides of the equation to solve for x. This step was done correctly.
In step 2, Josephine correctly simplified the left side and the right side of the equation. This step was also done correctly.
In step 3, Josephine made an error. She subtracted 6 from 7 to get x = 7-6 = 1. However, the correct subtraction should be x = -6 + 7 = 1.
Therefore, in step 3, Josephine made an error.
The correct answer is Option D - step 3.
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Step 1: √(x+6)^2 = √49
no
Step 1: √(x+6)^2 = +or-√49
so
x + 6 = 7
or
x + 6 = -7
x = 1
or x = - 13