Final answer:
To solve the quadratic equation by completing the square, you rearrange it to create a perfect square trinomial, then solve for the variable by taking the square root of both sides. For the equation p² + 8p + 13 = 0, the solutions are p = -4 + √3 and p = -4 - √3, which correspond to OPTION 1 and OPTION 2 respectively.
Step-by-step explanation:
Solving Quadratic Equations by Completing the Square
To solve the quadratic equation p² + 8p + 13 = 0 by completing the square, we must first arrange the equation in the form of (p + b/2a)² = -c/a + (b/2a)², which then allows us to find the value of p. Start by transferring the constant to the other side of the equation:
p² + 8p = -13
Next, add the square of half the coefficient of p (which is 4) to both sides:
(p + 4)² = 16 - 13
(p + 4)² = 3
Now take the square root of both sides, remembering to include both the positive and negative roots:
p + 4 = ±√3
Solve for p by subtracting 4 from both sides:
p = -4 + √3 or p = -4 - √3
Both options OPTION 1 and OPTION 2 are the correct solutions to this equation.