Question

Amira is solving the equation x2 – 6x = 1. Which value must be added to both sides of the equation to make the left side a perfect-square trinomial?

Answer 1

To make the left side of the equation x² – 6x = 1 a perfect-square trinomial, one must add 9 to both sides. This transforms the equation into (x - 3)² = 10.

Step-by-step explanation:

The student is asking how to make the left side of the equation x² – 6x = 1 a perfect-square trinomial. To do this, we must add the square of half the coefficient of x to both sides. The coefficient of x is -6, so half of this is -3, and the square of -3 is 9. Therefore, we must add 9 to both sides of the equation to form a perfect-square trinomial.

The equation then becomes x² – 6x + 9 = 1 + 9, which simplifies to (x - 3)² = 10. This transformed equation now has a left side that is a perfect square, specifically the square of (x - 3).

Answer 2

We have to add 9 on both sides of the equation.

Step-by-step explanation:

The given equation is
`x^2 - 6x = 1`

Let's identify the value of "b" by comparing the general form of quadratic equation
`ax^2 + bx + c = 0`

Here the value of b = -6

To make it perfect square trinomial, we have to divide b value by 2 and make it square. Then we have to add it on both side of the equation.

(b/2) = (-6/2)^2 = (-3)^2 = -3*-3 = 9

So we need to add 9 on both sides of the equation in order to make it perfect square.

`x^2 - 6x + 9 = 1 + 9\\(x -3)^2 = 10`