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.

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}

**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****By the way, there was a mistake on the PARCC answer key. Apparently, Pearson and PARCC's multi-million dollar industry thought the correct answer was B, as noted below. My low budget experience says it is C., as noted above. You be the judge!**

*- Algebra House*