Answer:
1) Now, the equation is in the form (x + a)² = b, where (x - 7)² is the perfect square trinomial.
2) the correct answer is A. x = 7 ± √5
Step-by-step explanation:
1) To rewrite the equation by completing the square, we need to make the left side of the equation a perfect square trinomial.
Starting with the given equation:
-34 = x² - 14x + 10
First, we move the constant term (-34) to the right side of the equation:
x² - 14x + 10 = -34
Next, we add the square of half the coefficient of x to both sides of the equation. In this case, the coefficient of x is -14, so half of it is -7. The square of -7 is 49.
x² - 14x + 49 + 10 = -34 + 49
Simplifying the equation:
(x - 7)² + 10 = 15
Now, the equation is in the form (x + a)² = b, where (x - 7)² is the perfect square trinomial.
2) To find the solutions to the equation, we can now take the square root of both sides:
√[(x - 7)² + 10] = √15
Taking the square root of (x - 7)² gives us:
x - 7 = ±√(15 - 10)
Simplifying:
x - 7 = ±√5
To isolate x, we add 7 to both sides of the equation:
x = 7 ± √5
Therefore, the solutions to the equation are:
A. x = 7 + √5
B. x = 7 - √5
So, the correct answer is A. x = 7 ± √5.
