Questions: Use the zero-factor property to solve the equation. 9 x^2 = 22 x - 8 The solutions set is . (Use a comma to separate answers. Type repeated roots only once.)

Solution Steps

To solve the quadratic equation using the zero-factor property, we need to:

1. Move all terms to one side of the equation to set it to zero.
2. Factor the quadratic expression.
3. Set each factor equal to zero and solve for $x$.

1. Rewrite the equation in standard form: $9x^2 - 22x + 8 = 0$.
2. Factor the quadratic expression.
3. Solve for $x$ by setting each factor to zero.

We start with the given equation: $$9x^2 = 22x - 8$$ Rearranging it to standard form gives: $$9x^2 - 22x + 8 = 0$$

Next, we factor the quadratic expression $9x^2 - 22x + 8$. The factors of this expression are: $$(9x - 2)(x - 4) = 0$$

Using the zero-factor property, we set each factor equal to zero:

1. $9x - 2 = 0$ leads to $x = \frac{2}{9}$
2. $x - 4 = 0$ leads to $x = 4$

Final Answer