Question

A student solved the equation x²+ 5x -60 = 5x +4. The student's work is shown below.

Determine if the student made an error. If so, explain their error AND solve for the correct solutions.

Answer 1

Answer: x = ±8

Explanation:

The given equation is:

x² + 5x - 60 = 5x + 4

The student's work shows that they simplified the equation correctly to:

x² - 64 = 0

However, their factorization of the resulting equation is incorrect. Factoring x² - 64 using difference of squares we get:

(x + 8)(x - 8) = 0

So, the solutions for x are x = -8 and x = 8. The student's solutions of x = ±32 are incorrect.

Therefore, the student made an error in factoring the equation, and the correct solutions for x are x = -8 and x = 8.

Answer 2

x = -8, 8

Explanation:

The student did make an error. When factoring
`x^2-64`, they used incorrect factors. Using FOIL method, the students factored equation would become
`x^2 +32x-32x-1024 = x^2-1024`, which is not
`x^2-64`.

Instead, the factors 8 and -8 should be used.

`x^(2) +5x-60=5x+4\\x^2 +5x - 64=5x\\x^2-64=0\\(x+8)(x-8)=0\\x=-8, 8`