Question

bao yu is completing the square to solve the polynomial equation.\\(x^2 - x - 3 = 0\\) what should be her first step? \\(\bigcirc\\) adding \\(-x\\) to both sides of the equation \\(\bigcirc\\) adding \\(-3\\) to both sides of the equation \\(\bigcirc\\) isolating the first term, \\(x^2\\) \\(\bigcirc\\) isolating the constant, \\(-3\\)

Explanation:

To solve a quadratic equation by completing the square, the first step is to isolate the constant term (the term without the variable) on one side of the equation. For the equation \(x^{2}-x - 3=0\), we need to move the constant \(- 3\) to the other side. This is done by adding \(3\) to both sides (or equivalently, isolating the constant \(-3\) by moving it to the right - hand side). Let's analyze the options:

• Option 1: Adding \(-x\) to both sides will not help in completing the square. It will complicate the equation further as we will have \(x^{2}-2x - 3=-x\), which is not a step in completing the square.
• Option 2: Adding \(-3\) to both sides will give \(x^{2}-x - 6=-3\), which is not a valid step for completing the square.
• Option 3: Isolating the first term \(x^{2}\) is not the first step in completing the square. We need to isolate the constant term first.
• Option 4: Isolating the constant \(-3\) (by adding \(3\) to both sides of the equation \(x^{2}-x - 3 = 0\) to get \(x^{2}-x=3\)) is the correct first step for completing the square.

Answer:

isolating the constant, \(-3\)