Questions: 4(x-1)^2-9(x-1)=-2 Step 1. Identify the quadratic form Let t= We now have: 4t^2-9t=-2 Step 2. Factor Factor this and solve for t to get t= and Step 3. Solve for x We have solved for t now we need to use this value for t to help us solve for x. Revisit step 1 to remind you of the relationship between t and x. Type your answers from smallest to largest. x=

4(x-1)^2-9(x-1)=-2

Step 1. Identify the quadratic form
Let t= We now have:
4t^2-9t=-2

Step 2. Factor
Factor this and solve for t to get t= and

Step 3. Solve for x
We have solved for t now we need to use this value for t to help us solve for x. Revisit step 1 to remind you of the relationship between t and x. Type your answers from smallest to largest.
x=

Transcript text: \[ 4(x-1)^{2}-9(x-1)=-2 \] Step 1. Identify the quadratic form Let $t=$ $\square$ We now have: \[ 4 t^{2}-9 t=-2 \] Step 2. Factor Factor this and solve for $t$ to get $t=$ $\square$ and $\square$ Step 3. Solve for $x$ We have solved for $t$ now we need to use this value for $t$ to help us solve for $x$. Revisit step 1 to remind you of the relationship between $t$ and $x$. Type your answers from smallest to largest. $x=$ $\square$

Solution

Solution Steps

Step 1: Identify the Quadratic Form

Let $ t = x - 1 $. Substitute $ t $ into the equation: \[ 4t^{2} - 9t = -2 \]

Step 2: Rearrange and Factor

Move all terms to one side to form a standard quadratic equation: \[ 4t^{2} - 9t + 2 = 0 \] Factor the quadratic equation: \[ (4t - 1)(t - 2) = 0 \] Solve for $ t $: \[ t = \frac{1}{4} \quad \text{and} \quad t = 2 \]

Step 3: Solve for $ x $

Recall that $ t = x - 1 $. Substitute the values of $ t $ back to solve for $ x $:

For $ t = \frac{1}{4} $: \[ x - 1 = \frac{1}{4} \implies x = 1 + \frac{1}{4} = \frac{5}{4} \]
For $ t = 2 $: \[ x - 1 = 2 \implies x = 1 + 2 = 3 \] Thus, the solutions for $ x $ are: \[ x = \frac{5}{4} \quad \text{and} \quad x = 3 \]