Solve the following quadratic equation using the perfect square trinomial pattern: x2+54x=−729 .(1 point) x=

Answer 1

To solve the quadratic equation using the perfect square trinomial pattern, we need to complete the square by adding and subtracting a constant term.

First, let's rewrite the equation in the form: x^2 + 54x + ___ = -729 + ___

The perfect square trinomial pattern is (a + b)^2 = a^2 + 2ab + b^2.

In this case, the equation can be rewritten as:

x^2 + 54x + (27)^2 = -729 + (27)^2

x^2 + 54x + 729 = -729 + 729

x^2 + 54x + 729 = 0

Now we can see that the left side of the equation is a perfect square trinomial (x + 27)^2.

So, the equation can be written as:

(x + 27)^2 = 0

Taking the square root of both sides, we get:

x + 27 = 0 or x + 27 = 0

Solving for x:

x = -27 or x = -27

Therefore, the solutions to the quadratic equation x^2 + 54x = -729 are x = -27 and x = -27.