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.)

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.)
failed

Solution

failed
failed

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 x .
Solution Approach
  1. Rewrite the equation in standard form: 9x222x+8=0 9x^2 - 22x + 8 = 0 .
  2. Factor the quadratic expression.
  3. Solve for x x by setting each factor to zero.
Step 1: Rewrite the Equation

We start with the given equation: 9x2=22x8 9x^2 = 22x - 8 Rearranging it to standard form gives: 9x222x+8=0 9x^2 - 22x + 8 = 0

Step 2: Factor the Quadratic

Next, we factor the quadratic expression 9x222x+8 9x^2 - 22x + 8 . The factors of this expression are: (9x2)(x4)=0 (9x - 2)(x - 4) = 0

Step 3: Solve for x x

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

  1. 9x2=0 9x - 2 = 0 leads to x=29 x = \frac{2}{9}
  2. x4=0 x - 4 = 0 leads to x=4 x = 4

Final Answer

The solution set is: {29,4} \boxed{\left\{ \frac{2}{9}, 4 \right\}}

Was this solution helpful?
failed
Unhelpful
failed
Helpful