How do you solve #2x^2 12x + 11=0# by completing the square?
Divide first by two to obtain:
in order for us to write
Add three to each side to obtain
Generally speaking,
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To solve the quadratic equation (2x^2  12x + 11 = 0) by completing the square, follow these steps:

Move the constant term to the other side of the equation: [2x^2  12x = 11]

Divide the entire equation by the coefficient of (x^2) to make the leading coefficient (1): [x^2  6x = \frac{11}{2}]

To complete the square, take half of the coefficient of (x), square it, and add it to both sides of the equation: [x^2  6x + (6/2)^2 = \frac{11}{2} + (6/2)^2] [x^2  6x + 9 = \frac{11}{2} + 9]

Simplify: [x^2  6x + 9 = \frac{11}{2} + \frac{36}{2}] [x^2  6x + 9 = \frac{25}{2}]

Rewrite the left side as a perfect square: [(x  3)^2 = \frac{25}{2}]

Take the square root of both sides: [x  3 = \pm \sqrt{\frac{25}{2}}]

Simplify the square root: [x  3 = \pm \frac{5}{\sqrt{2}}]

To rationalize the denominator, multiply the numerator and denominator by (\sqrt{2}): [x  3 = \pm \frac{5\sqrt{2}}{2}]

Add (3) to both sides to isolate (x): [x = 3 \pm \frac{5\sqrt{2}}{2}]
Therefore, the solutions to the equation (2x^2  12x + 11 = 0) by completing the square are (x = 3 + \frac{5\sqrt{2}}{2}) and (x = 3  \frac{5\sqrt{2}}{2}).
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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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