Question

Solve the equation y = x² - 8x = 19 by completing the square.

a) y = (x - 4)² - 35
b) y = (x - 4)² + 35
c) y = (x + 4)² - 35
d) y = (x + 4)² + 35

Answer 1

To solve the quadratic equation by completing the square, we adjust the equation to form a perfect square trinomial, which reveals that the correct option is a) y = (x - 4)² - 35.

Step-by-step explanation:

To solve the equation y = x² - 8x = 19 by completing the square, we start by moving the constant term to the right side of the equation:

x² - 8x = 19

Now, to complete the square, we take half of the coefficient of x, which is 8, divide it by 2 to get 4, and then square it to get 16. We'll add and subtract this number inside the equation:

x² - 8x + 16 - 16 = 19

Adding 16 and then subtracting 16 does not change the value of the equation, but it allows us to write the left side as a perfect square:

(x - 4)² - 16 = 19

Now we need to get y by itself, so we add 16 to both sides:

(x - 4)² = 19 + 16

(x - 4)² = 35

Finally, we can write the equation in the form of:

y = (x - 4)² - 35

Therefore, the correct option is a) y = (x - 4)² - 35.