To solve the quadratic equation x² + 54x = -729 using the perfect square trinomial pattern, we need to rewrite the equation in the form of (x + a)² = b, where a and b are constants.
First, we move the constant term (-729) to the right side of the equation:
x² + 54x + 729 = 0
Next, we observe that the coefficient of x (54) is twice the product of the square root of the coefficient of x² (1) and the constant term (-27). This suggests that we can rewrite the equation as a perfect square trinomial.
(x + 27)² = 0
Now, we can solve for x by taking the square root of both sides of the equation:
x + 27 = ±√0
x + 27 = 0 or x + 27 = 0
Solving for x in each case:
Case 1: x + 27 = 0
x = -27
Case 2: x + 27 = 0
x = -27
Therefore, the solution to the quadratic equation x² + 54x = -729 is x = -27.
Solve the following quadratic equation using the perfect square trinomial pattern: x² + 54x = -729.
1 answer
1 answer