Completing the Square Examples

Example 1
Solve by completing the square.

-x ^{2} + 6x + 13 = 0

Follow the steps for completing the square.

x ^{2} – 6x – 13 = 0

Be careful, because a = -1, not a = 1 like we need.

(x ^{2} – 6x + (3)^{2} ) – 13 – 9 = 0

is 3.

(x – 3)^{2} = 22

and }

Square completed.

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Example 2
Solve by completing the square.

2x ^{2} – x – 4 = 0

Start by clearing out the a term.

is

Make sure that you have added and subtracted your terms correctly. The fractions being squared can make this difficult.

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Example 3
Solve by completing the square.

Having a fraction for a doesn't really change anything.

x ^{2} + 10x + 2 = 0

Just multiply through to clear it out.

(x ^{2} + 10x + (5)^{2} ) + 2 – (5)^{2} = 0

is 5.

(x + 5)^{2} = 25 – 2

and

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