Rewrite the equation by completing the square.

Ask by Mathis Hammond. in the United States

Jan 23,2025

Question

Rewrite the equation by completing the square. $$ x^{2}-6 x-16=0 $$ $$ (x+\square)^{2}=\square $$

UpStudy AI · Accepted Answer

To rewrite the equation $$ x^{2} - 6x - 16 = 0 $$ by completing the square, follow these steps:

1. **Move the constant term to the other side:**
   $$
   x^{2} - 6x = 16
   $$

2. **Complete the square for the quadratic expression on the left:**
   - Take half of the coefficient of $$ x $$, which is $$ -6 $$, resulting in $$ -3 $$.
   - Square this value: $$ (-3)^2 = 9 $$.
   - Add this square to both sides of the equation:
     $$
     x^{2} - 6x + 9 = 16 + 9
     $$

3. **Simplify both sides:**
   $$
   (x - 3)^2 = 25
   $$

So, the equation rewritten by completing the square is:

$$
(x - 3)^2 = 25
$$
$$ (x - 3)^2 = 25 $$

Rewrite the equation by completing the square.

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