Question

Bao Yu is completing the square to solve the polynomial equation. x2 – x – 3 = 0 What should be her first step

Answer 1

Answer:

collect the like terms

Step-by-step explanation:

2x-x-3=0

x-3=0

Answer 2

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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