Math Problem Statement
complete the swuare
Solve x^2 - 4x - 13 = 0 by completing the square.
Solution
To solve by completing the square, follow these steps:
Step 1: Rearrange the equation
Move the constant term () to the other side of the equation:
Step 2: Complete the square
Take half of the coefficient of , square it, and add it to both sides. The coefficient of is , so: Add to both sides:
Step 3: Solve for
Take the square root of both sides:
Step 4: Isolate
Add to both sides:
Final Answer:
The solutions are:
If you have any further questions, let me know!
Related Questions:
- What does "completing the square" help us understand about quadratic equations?
- How can we verify that the solutions satisfy the original equation?
- What are some real-world applications of solving quadratic equations like this?
- How does completing the square relate to the quadratic formula?
- Could the solutions be expressed in decimal form? What would they approximately be?
Tip:
Always double-check your calculations when completing the square, especially when determining the term to add!
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Math Problem Analysis
Mathematical Concepts
Algebra
Completing the Square
Quadratic Equations
Formulas
(x + p)^2 = q
Quadratic solutions: x = h ± √k
Theorems
The Square Root Property
Suitable Grade Level
Grades 8-10