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:

Step1: Recall Completing the Square

To complete the square for \(ax^2 + bx + c = 0\), first isolate the constant term \(c\) (move it to the other side) so that the quadratic and linear terms are on one side. For \(x^2 - x - 3 = 0\), the constant is \(-3\).

Step2: Analyze Options

• Adding \(-x\) or \(-3\) is incorrect as it doesn't follow completing the square steps.
• Isolating \(x^2\) is not the first step.
• Isolating the constant \(-3\) (by adding \(3\) to both sides: \(x^2 - x = 3\)) is the first step in completing the square.

Answer:

isolating the constant, \(-3\)