Question

What would be the appropriate next step to solve the following equation by completing the square? Equation: x^2 – 14x + 13 = 0

Options:
a) x^2 – 14x = -13
b) x^2 – 14x + 7^2 = -13 + 7^2
c) x^2 – 14x + 49 = 36
d) x^2 = 14x + 13

Answer 1

The appropriate next step to solve the equation by completing the square is option b) x^2 – 14x + 7^2 = -13 + 7^2. The next step involves adding the square of half the coefficient of x to both sides of the equation.

Step-by-step explanation:

The appropriate next step to solve the equation by completing the square is option b) x^2 – 14x + 7^2 = -13 + 7^2.

Step 1: Move the constant term to the right side of the equation: x^2 – 14x = -13.

Step 2: Add the square of half the coefficient of x to both sides of the equation: x^2 – 14x + (14/2)^2 = -13 + (14/2)^2.

Step 3: Simplify both sides of the equation: x^2 – 14x + 49 = 36.