Math Problem Statement
Solution
Let's solve the quadratic equation by completing the square.
Step 1: Write the equation in the form .
We already have: Subtract 16 from both sides:
Step 2: Complete the square.
To complete the square, take half of the coefficient of , which is , divide by 2, and square it.
Add 16 to both sides to complete the square:
Now the left side is a perfect square trinomial:
Step 3: Solve for .
Take the square root of both sides:
Solve for :
Thus, the solution is:
Would you like more details on any step or have any questions?
Related Questions:
- How do you complete the square for a general quadratic equation?
- What if the quadratic equation had a different constant term, like ?
- Can you apply completing the square for equations where the coefficient of is not 1?
- How does completing the square relate to the quadratic formula?
- What are other methods for solving quadratic equations?
Tip:
When completing the square, always ensure the coefficient of is 1. If it's not, divide the whole equation by the coefficient before proceeding!
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Math Problem Analysis
Mathematical Concepts
Algebra
Completing the Square
Quadratic Equations
Formulas
(x - b/2)^2 = (b/2)^2 - c
Theorems
The method of completing the square to solve quadratic equations
Suitable Grade Level
Grades 8-10