Math Problem Statement
Solution
To determine which number must be added to complete the square for the equation , we first isolate the quadratic and linear terms:
Next, we add the square of half the coefficient of to both sides. The coefficient of is 9, so half of it is , and its square is .
We add to both sides of the equation:
Now, we need to find the number that must be added to complete the square on the left side. This number is .
Thus, the answer is:
Do you want details or have any questions? Here are five more questions you might ask:
- How do you determine the number to complete the square in a quadratic equation?
- Why is completing the square useful for solving quadratic equations?
- How do you solve a quadratic equation once it is in completed square form?
- What is the relationship between completing the square and the vertex form of a quadratic equation?
- Can completing the square be used for solving quadratic inequalities?
Tip: When completing the square, remember to add the same value to both sides of the equation to maintain the equality. This step is crucial for correctly solving the equation.
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Math Problem Analysis
Mathematical Concepts
Quadratic Equations
Completing the Square
Formulas
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Theorems
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Suitable Grade Level
Grades 10-12