Question
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Solve by completing the square.
Write your answers as integers, proper or improper fractions in simplest form, or decir
rounded to the nearest hundredth.

Ask by Reyes Barker. in the United States
Mar 14,2025

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Tutor-Verified Answer

Answer

The solutions are and .

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The Deep Dive

To solve the equation by completing the square, we first rearrange the equation:
Next, we focus on the quadratic part, . To complete the square, we take half of the coefficient of (which is 6), square it, and add it to both sides:
  1. Half of 6 is 3, and .
  2. Add 9 to both sides:
This simplifies to:
Now, to solve for , we take the square root of both sides:
Subtract 3 from both sides:
Thus, the solutions are:
Approximating , which is about 7.62, we get:
So round your final answer as needed:

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