How do you solve the equation #x^2+6x+13=0# by completing the square?
The squares identity difference can be expressed as follows:
Hence:
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To solve the equation ( x^2 + 6x + 13 = 0 ) by completing the square, follow these steps:

Move the constant term to the other side of the equation: [ x^2 + 6x = 13 ]

To complete the square, take half of the coefficient of ( x ) (which is 6), square it, and add it to both sides of the equation: [ x^2 + 6x + (6/2)^2 = 13 + (6/2)^2 ] [ x^2 + 6x + 9 = 13 + 9 ]

Simplify both sides of the equation: [ x^2 + 6x + 9 = 4 ]

Rewrite the left side of the equation as a perfect square trinomial: [ (x + 3)^2 = 4 ]

Take the square root of both sides of the equation: [ x + 3 = \pm \sqrt{4} ]

Since the square root of a negative number is imaginary, there are no real solutions for ( x ).
Therefore, the equation ( x^2 + 6x + 13 = 0 ) does not have real solutions.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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