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.)
Transcript text: Use the zero-factor property to solve the equation.
\[
9 x^{2}=22 x-8
\]
The solutions set is $\square$ \}.
(Use a comma to separate answers. Type repeated roots only once.)
Solution
Solution Steps
To solve the quadratic equation using the zero-factor property, we need to:
Move all terms to one side of the equation to set it to zero.
Factor the quadratic expression.
Set each factor equal to zero and solve for x.
Solution Approach
Rewrite the equation in standard form: 9x2−22x+8=0.
Factor the quadratic expression.
Solve for x by setting each factor to zero.
Step 1: Rewrite the Equation
We start with the given equation:
9x2=22x−8
Rearranging it to standard form gives:
9x2−22x+8=0
Step 2: Factor the Quadratic
Next, we factor the quadratic expression 9x2−22x+8. The factors of this expression are:
(9x−2)(x−4)=0
Step 3: Solve for x
Using the zero-factor property, we set each factor equal to zero: