Answer:
Hi,
Explanation:
To rewrite the equation x² + 5x + 5/4 = 0 in the form (x-p) = q, we can complete the square.
Step 1: Move the constant term to the other side of the equation:
x^2 + 5x = -5/4
Step 2: Take half of the coefficient of the x term, square it, and add it to both sides of the equation:
x^2 + 5x + (5/2)^2 = -5/4 + (5/2)^2
Simplifying, we get:
x^2 + 5x + 25/4 = -5/4 + 25/4
Step 3: Factor the left side of the equation:
(x + 5/2)^2 = 20/4
Simplifying further, we get:
(x + 5/2)^2 = 5
Step 4: Take the square root of both sides of the equation:
x + 5/2 = ±√5
Step 5: Solve for x by subtracting 5/2 from both sides:
x = -5/2 ± √5
Therefore, the equation x^2 + 5x + 5/4 = 0 can be rewritten in the form (x-p) = q as:
(x + 5/2) = ±√5
I hope this helps! Let me know if you have any further questions.