Question

Consider this equation 5x-1=x^2+2x+1. Which of the following values of x make the equation true? Select the two correct values A. -2B. -1C. 0D. 1E. 2

Answer 1

The values are 1 and 2. Option D and E

From the information given, we have that the equation is given as;

5x - 1=x²+2x+1

collect the like terms, we have;

x² + 2x - 5x + 1 + 1 = 0

add the like terms, we get;

x² - 3x + 2 = 0

Now, let us solve the quadratic equation, we have;

x² -2x - x + 2 = 0

Group the equation in pairs, we have;

(x² -2x) - (x + 2) = 0

x(x - 2) - 1(x -2) = 0

Then,

x - 1 = 0, x = 1

x -2 = 0, x = 2

Answer 2

Given:

`5x-1=x^2+2x+1`
`\begin{gathered} x^2+2x+1-5x+1=0 \\ x^2-3x+2=0 \\ (x-2)(x-1)=0 \\ x=1,2 \end{gathered}`

Option D and E are the final answers.