Math Problem Statement
Solution
Let's go through the problem step by step to solve it by completing the square.
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Starting with the given equation: First, subtract 4 from both sides:
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Now, complete the square. Take half of the coefficient of , which is , divide by 2 to get , and then square it to get . Add 16 to both sides: Simplifying:
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Rewrite the left-hand side as a perfect square:
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Solve for by taking the square root of both sides: This gives two solutions:
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Solve for in both cases:
Thus, the solutions are or .
Would you like more details about any step? Here are some related questions you might find helpful:
- How do you derive the value to add when completing the square?
- Why do we take the square root of both sides when solving?
- How do you recognize when to complete the square vs using other methods?
- Can this method be applied to equations with larger coefficients or constants?
- How can you verify that your solutions are correct?
Tip: Always check your final answers by substituting them back into the original equation to ensure they satisfy it!
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Math Problem Analysis
Mathematical Concepts
Algebra
Completing the Square
Quadratic Equations
Formulas
Completing the Square formula
Theorems
Properties of equality
Square root principle
Suitable Grade Level
Grades 8-10