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​Algebra 1   State Test Practice

Solve quadratic equations by completing the square

1/25/2015

 
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
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
​

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