How do you solve the equation #x^2+x+1/4=9/16# by completing the square?
reorganize in the manner shown below
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To solve the equation (x^2 + x + \frac{1}{4} = \frac{9}{16}) by completing the square, follow these steps:

Move the constant term to the other side of the equation: [x^2 + x = \frac{9}{16}  \frac{1}{4}]

Find the common denominator and combine the fractions on the right side: [x^2 + x = \frac{9}{16}  \frac{4}{16} = \frac{5}{16}]

Complete the square by adding and subtracting (\left(\frac{1}{2} \cdot 1\right)^2) to the left side of the equation: [x^2 + x + \left(\frac{1}{2}\right)^2 = \frac{5}{16} + \left(\frac{1}{2}\right)^2]

Simplify both sides of the equation: [x^2 + x + \frac{1}{4} = \frac{5}{16} + \frac{1}{4}]

Factor the left side of the equation: [\left(x + \frac{1}{2}\right)^2 = \frac{5}{16} + \frac{4}{16}]

Combine the fractions on the right side: [\left(x + \frac{1}{2}\right)^2 = \frac{9}{16}]

Take the square root of both sides: [x + \frac{1}{2} = \pm \sqrt{\frac{9}{16}}]

Simplify the right side: [x + \frac{1}{2} = \pm \frac{3}{4}]

Solve for (x): [x = \frac{1}{2} \pm \frac{3}{4}]

Simplify the expressions: [x = \frac{1}{2} + \frac{3}{4} \quad \text{or} \quad x = \frac{1}{2}  \frac{3}{4}]
[x = \frac{1}{4} \quad \text{or} \quad x = \frac{5}{4}]
So, the solutions to the equation (x^2 + x + \frac{1}{4} = \frac{9}{16}) are (x = \frac{1}{4}) and (x = \frac{5}{4}).
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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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