Answer:
Explanation:
Alright man, I got you.
So here is step-by-step
To solve the equation x^2 + 14x - 51 = 0 by completing the square, follow these steps:
Step 1: Move the constant term to the right-hand side
x^2 + 14x = 51
Step 2: Take half of the coefficient of x, square it, and add it to both sides of the equation
To find half of the coefficient of x, divide it by 2:
(14 / 2) = 7
Then square 7:
7^2 = 49
Add 49 to both sides of the equation:
x^2 + 14x + 49 = 51 + 49
Simplifying the right-hand side:
x^2 + 14x + 49 = 100
Step 3: Factor the left-hand side as a perfect square
The left-hand side is now a perfect square trinomial, which can be factored as:
(x + 7)^2 = 100
Step 4: Take the square root of both sides of the equation
Taking the square root of both sides of the equation gives:
x + 7 = ±10
Step 5: Solve for x
Subtracting 7 from both sides of the equation gives:
x = -7 ± 10
Therefore, the solutions to the equation x^2 + 14x - 51 = 0 are:
x = -7 + 10 = 3
or
x = -7 - 10 = -17