Complete the square to write 16*t*² - 96*t* + 48 = 0 as

To complete the square for the quadratic equation \( 16t^2 - 96t + 48 = 0 \), follow these steps:

### Step 1: Divide the entire equation by 16.
First, simplify the equation by dividing all terms by 16 to make the coefficient of \( t^2 \) equal to 1.

\[
t^2 - 6t + 3 = 0
\]

### Step 2: Move the constant term to the right side.
To prepare for completing the square, isolate the constant term:

\[
t^2 - 6t = -3
\]

### Step 3: Complete the square.
Take half of the coefficient of \( t \) (which is -6), square it, and add it to both sides of the equation. Half of -6 is -3, and squaring it gives \( (-3)^2 = 9 \).

Add 9 to both sides:

\[
t^2 - 6t + 9 = -3 + 9
\]

This simplifies to:

\[
(t - 3)^2 = 6
\]

### Step 4: Write the equation in completed square form.
Now the equation is written as:

\[
(t - 3)^2 = 6
\]

Thus, the equation \( 16t^2 - 96t + 48 = 0 \) can be written as \( (t - 3)^2 = 6 \) after completing the square.

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Would you like more details or explanations on this process?

Here are five related questions for further practice:
1. Complete the square for \( 9x^2 - 12x + 4 = 0 \).
2. Solve \( t^2 - 6t + 3 = 0 \) using the quadratic formula.
3. Convert \( t^2 + 4t - 5 = 0 \) into completed square form.
4. Write the equation \( 25y^2 - 30y + 9 = 0 \) in completed square form.
5. Solve \( (t - 3)^2 = 6 \) for \( t \).

**Tip:** When completing the square, always make sure the coefficient of \( t^2 \) is 1 before proceeding.

Complete the square to write 16*t*² - 96*t + 48 = 0 as

Step-by-step guide to completing the square for the quadratic equation 16t² - 96t + 48 = 0. Learn how to rewrite this equation in the form (t - 3)² = 6. Ideal for students in Grades 9-11, this problem covers key algebraic concepts like completing the square.

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