Question

Solve the following quadratic equation using the perfect square trinomial pattern: x ^ 2 + 54x = - 729 x = box

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the quadratic equation using the perfect square trinomial pattern, we need to rewrite the equation in the form (x + a)^2 = b.

Given equation: x^2 + 54x = -729

To rewrite it in the form (x + a)^2 = b, we need to complete the square.

Step 1: Take half of the coefficient of x and square it.
Half of 54 is 27, and (27)^2 = 729.

Step 2: Add the result from step 1 to both sides of the equation.
x^2 + 54x + 729 = -729 + 729
x^2 + 54x + 729 = 0

Step 3: Rewrite the left side of the equation as a perfect square trinomial.
(x + 27)^2 = 0

Now, we can solve for x. Taking the square root of both sides:

x + 27 = 0
x = -27

The solution to the quadratic equation x^2 + 54x = -729 is x = -27.