Final answer:
To complete the square for the equation x² + 16x - 2 = 11, the equation is rearranged to x² + 16x - 13 = 0, and then (16/2)² = 64 is added and subtracted to form (x + 8)² - 77 = 0, which is the completed square form.
Step-by-step explanation:
The student is asking to rewrite the equation x² + 16x - 2 = 11 by completing the square. To complete the square, one must first ensure that the quadratic equation is in the form ax² + bx + c = 0. From the given equation, we can subtract 11 from both sides to get x² + 16x - 13 = 0. Then we want to form a perfect square trinomial from the first two terms.
You can complete the square by adding and subtracting (b/2a)², where 'a' is the coefficient of x² and 'b' is the coefficient of x. So, for the equation given:
- a = 1
- b = 16
- (b/2a)² = (16/2*1)² = 64
Now we add and subtract 64 and rearrange:
x² + 16x + 64 - 64 - 13 = 0
Which becomes:
(x + 8)² - 77 = 0
So the original equation, completed square, is (x + 8)² = 77.