Section C Section C Checkpoint

Problem 1

Complete the square to solve the equations. Give exact solutions.

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Solution

$x = 1$ and $x = \text{-}3$ . Sample reasoning: Completing the square leads to $(x+1)^2 = 4$ . This means that $x + 1 = 2$ and $x + 1 = \text{-}2$ .
$x = \text{-}3\pm\sqrt{6}$ . Sample reasoning: Completing the square leads to $(x+3)^2 = 6$ . This means that $x + 3 = \pm \sqrt{6}$ .

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Sample Response

$x = 1$ and $x = \text{-}3$ . Sample reasoning: Completing the square leads to $(x+1)^2 = 4$ . This means that $x + 1 = 2$ and $x + 1 = \text{-}2$ .
$x = \text{-}3\pm\sqrt{6}$ . Sample reasoning: Completing the square leads to $(x+3)^2 = 6$ . This means that $x + 3 = \pm \sqrt{6}$ .

Select all of the equations that are equivalent to

x = 3 \pm \sqrt{2}

x = \sqrt{5}

x = \sqrt{\text{-}1}

x = 3 + \sqrt{2}

x = \sqrt{\pm 6}

x = 3 - \sqrt{2}

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Solution

C, E

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Sample Response

C, E