Find the equation that is equivalent to the quadratic equation shown.
x² - 6x - 27 = 0
A.) x(x - 3) = 27
B.) (x - 6)² = 63
C.) (x - 3)² = 36
D.) (x - 3)² = 28
x² - 6x - 27 = 0
A.) x(x - 3) = 27
B.) (x - 6)² = 63
C.) (x - 3)² = 36
D.) (x - 3)² = 28
It appears, completing the square was used to arrive at one of the given answer choices.
To complete the square:
x² - 6x - 27 = 0
x² - 6x = 27 {added 27 to each side to get into the form ax² + bx = c}
x² - 6x + 9 = 27 + 9 {took half of the coefficient of x, squared it, and added it to both sides}
x² - 6x + 9 = 36 {combined like terms on the right side}
(x - 3)² = 36 {factored the perfect square trinomial on the left into the square of a binomial}
C.) (x - 3)² = 36
To complete the square:
x² - 6x - 27 = 0
x² - 6x = 27 {added 27 to each side to get into the form ax² + bx = c}
x² - 6x + 9 = 27 + 9 {took half of the coefficient of x, squared it, and added it to both sides}
x² - 6x + 9 = 36 {combined like terms on the right side}
(x - 3)² = 36 {factored the perfect square trinomial on the left into the square of a binomial}
C.) (x - 3)² = 36
