The equation x^2 - 8x - 5 = 0 xan be transformed into the equation (x - p)^2 = q, where p and q are real numbers. What is the value of q?
q = 21
To transform the equation x^2 - 8x - 5 = 0 into the equation (x - p)^2 = q, we need to complete the square. The general form of a quadratic equation in the form (x - p)^2 = q is obtained by expanding (x - p)(x - p) using the FOIL method.
Let's start by completing the square for the given equation x^2 - 8x - 5 = 0:
Step 1: Move the constant term (-5) to the right side of the equation:
x^2 - 8x = 5
Step 2: To complete the square, take half of the coefficient of x (-8/2 = -4) and square it: (-4)^2 = 16.
Step 3: Add the value obtained in step 2 (16) to both sides of the equation:
x^2 - 8x + 16 = 5 + 16
(x - 4)^2 = 21
Now we have transformed the given equation into the form (x - p)^2 = q, where p = 4 and q = 21.
Therefore, the value of q is 21.
To transform the equation x^2 - 8x - 5 = 0 into the form (x - p)^2 = q, we need to complete the square. Here are the steps:
1. Move the constant term (-5) to the right side of the equation:
x^2 - 8x = 5
2. Take half of the coefficient of x (-8), square it, and add it to both sides of the equation:
x^2 - 8x + (-8/2)^2 = 5 + (-8/2)^2
x^2 - 8x + 16 = 5 + 16
x^2 - 8x + 16 = 21
3. Rewrite the left side of the equation as a perfect square:
(x - 4)^2 = 21
Now we have transformed the equation into the form (x - p)^2 = q, where p = 4 and q = 21. Therefore, the value of q is 21.