To transform the equation x^2 - 8x - 5 = 0 into the equation (x - p)^2 = q, we need to complete the square.
First, let's move the constant term to the right side:
x^2 - 8x = 5
Next, we want to find a value to add and subtract inside the parenthesis to create a perfect square on the left side. To do this, we take half of the coefficient of x (-8/2 = -4) and square it (16):
x^2 - 8x + 16 = 5 + 16
Simplifying the right side:
x^2 - 8x + 16 = 21
Now, we can write the left side as a perfect square:
(x - 4)^2 = 21
Comparing this equation to the equation (x - p)^2 = q, we can see that p = 4 and q = 21.
The equation
x
2
−
8
x
−
5
=
0
can be transformed into the equation
(
x
−
p
)
2
=
q
,
where
p
and
q
are real numbers.
What are the values of
p
and
q
?
1 answer