Solve the equation for all values of x by completing the square.x, squared, plus, 14, x, plus, 48, equals, 0x 2 +14x+48=0
Question
Solve the equation for all values of x by completing the square.
Given the equation:
Solution
1. Break Down the Problem
We need to solve the quadratic equation by completing the square.
2. Relevant Concepts
The method of completing the square involves rearranging the quadratic equation into the form .
3. Analysis and Detail
Step 1: Rearrange the equation To complete the square, we need to isolate the constant term:
Step 2: Find the term to complete the square Take half of the coefficient of (which is 14), square it, and add to both sides: Add 49 to both sides: This simplifies to:
Step 3: Rewrite the left side as a squared term
4. Verify and Summarize
Step 4: Take the square root of both sides
Step 5: Solve for
- leads to:
- leads to:
The solutions to the equation are and .
Final Answer
The solutions for the equation are:
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