Bao Yu's first step is to make the term with x of the form
-x=-2×(1/2)×x.
So that we get x²-x-3=0
⇒ x²-2×(1/2)×x -3=0
What is Completing the square method?
Completing the Square is a method for solving a quadratic equation by changing the form of the equation to a perfect square trinomial on the left side.
How to use the method on the given quadratic equation?
Given, x²-x-3=0
Step 1: Firstly make the term with x of the form
-x=-2×(1/2)×x
We get x²-x-3=0
⇒ x²-2×(1/2)×x -3=0
Step 2: Secondly, make add (1/2)² to both sides of the equation to make a perfect square (x-(1/2))² on the left side of the equation.
We get
x²-x-3=0
⇒ x²-2×(1/2)×x -3=0
⇒ x²-2×(1/2)×x +(1/2)²-3=(1/2)²
⇒ (x-(1/2))²=3+(1/4)=13/4
⇒ (x-(1/2))²=13/4
⇒ x-(1/2)=±(√13)/2 and the solution follows.
Thus, we complete the square to solve the polynomial equation x²-x-3=0. And the first step is to make the term with x of the form
-x=-2×(1/2)×x
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