Question

Ellen was solving the following equation, x2 - 8x+41 - 0 Which would be correct for the given methods?

Solving using the quadratic formula, she needs to subtract 41 on both sides
O When solving using square roots, she will need to complete the square on the left side
To complete the square, she will need to add -8 to both sides
O She cannot solve the equation because there are no x intercepts

Answer 1

Option A & B

- she needs to subtract 41 on both sides

-When solving using square roots, she will need to complete the square on the left side

Explanation:

We are given the equation;

x² - 8x + 41 = 0

To solve this with completing the square, the steps are;

1) divide the entire equation by the coefficient of x². Coefficient is 1 and so the equation remains the way it is.

2) We will rewrite the equation by taking the constant term to the right hand side.

To do this, we will subtract 41 from both sides to get;

x² - 8x + 41 - 41 = 0 - 41

x² - 8x = -41

3) We will now complete the square by adding the square of half of the coefficient of x to both sides of the equation.

Thus;

x² - 8x + (-8/2)² = -41 + (-8/2)²

x² - 8x + 16 = -41 + 16

x² - 8x + 16 = -25

4) We will write the left side as a square.

Thus;

(x - 4)² = -25

Looking at the options, we can see that the only 2 options that correspond to the steps above are;

- she needs to subtract 41 on both sides

-When solving using square roots, she will need to complete the square on the left side