How to complete the square where the coefficient of x^2 isn't 1
Автор: MathswithMissRowlands
Загружено: 2025-12-14
Просмотров: 3
Summary
The video provides a step-by-step explanation of the completing the square method applied to a quadratic equation where the coefficient of ( x^2 ) is not one. The process involves algebraic manipulation to transform the quadratic expression into a perfect square trinomial, enabling easier solution for ( x ).
Key Steps and Concepts
Factoring out the coefficient of ( x^2 ):
Since the coefficient of ( x^2 ) is 2 (not 1), factor 2 out of the terms involving ( x ), placing them inside a bracket. This isolates the quadratic and linear terms for easier manipulation.
Halving the coefficient of ( x ):
The coefficient of ( x ) inside the bracket is 4. To complete the square, take half of this coefficient (which is 2), then square it (resulting in 4). This step is critical because: [ (x - 2)^2 = x^2 - 4x + 4 ]
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