Question

Your teacher wrote out the steps for solving the equation x^(2)-18x+8=0 by completing the square as shown.

Fill in the blanks to show each of the correct steps and solutions to the equation. Write the solutions in simplest radical form, if needed.

Answer 1

The steps to solve the equation x^2 - 18x + 8 = 0 by completing the square are:

1. Move the constant term to the right side: x^2 - 18x = -8

2. Take half of the coefficient of x, square it, and add it to both sides of the equation:

x^2 - 18x + (-18/2)^2 = -8 + (-18/2)^2

x^2 - 18x + 81 = -8 + 81

3. Simplify the left side and the right side of the equation:

(x - 9)^2 = 73

4. Take the square root of both sides of the equation, remembering to include both the positive and negative square roots:

x - 9 = ± √73

5. Add 9 to both sides of the equation:

x = 9 ± √73

Therefore, the solutions to the equation x^2 - 18x + 8 = 0 are x = 9 + √73 and x = 9 - √73.

Explanation: