Answer:
{1, 7}
Step-by-step explanation:
Start with x^2 - 8x + 7 = 0.
We want to modify the first two terms to resemble x^2 - ax + b - b, where a is the coefficient (here -8) of the x term and b is the square of half of a.
Here, a = -8. Half of that is -4. The square of -4 is 16, and this is the value of b.
Write out x^2 - 8x as x^2 - 8x + 16 - 16. This is the perfect square of -4, added to x^2 - 8x and then subtracted from the result
Then the original equation, x^2 - 8x + 7 = 0, can be rewritten as:
x^2 - 8x + 16 - 16 + 7 = 0, and then as (x - 4)^2 - 9, or (x - 4)^2 = 9.
We want to solve this result for x. To do this, take the square root of both sides:
x - 4 = ±√9, or x - 4 = ±3.
Adding 4 to both sides, we get:
x = 4 ± 3. Thus, the solutions are x = 4 + 3 = 7 and x = 4 - 3 = 1.
