Solve the following quadratic
function by completing the square

Ask by Colon Stewart. in the United States

Jan 23,2025

Question

Solve the following quadratic function by completing the square $$ y=x^{2}-8 x+5 $$ $$ x=[?] \pm \sqrt{\square]} $$

UpStudy AI · Accepted Answer

To solve the quadratic equation $$ y = x^2 - 8x + 5 $$ by completing the square, follow these steps:

1. **Set the equation to zero** (to find the roots):
   $$
   x^2 - 8x + 5 = 0
   $$

2. **Move the constant term to the other side**:
   $$
   x^2 - 8x = -5
   $$

3. **Complete the square**:
   - Take half of the coefficient of $$ x $$, which is $$ -8 $$, so half is $$ -4 $$.
   - Square it: $$ (-4)^2 = 16 $$.
   - Add 16 to both sides to complete the square:
     $$
     x^2 - 8x + 16 = -5 + 16
     $$
     $$
     (x - 4)^2 = 11
     $$

4. **Solve for $$ x $$** by taking the square root of both sides:
   $$
   x - 4 = \pm \sqrt{11}
   $$
   $$
   x = 4 \pm \sqrt{11}
   $$

**Final Answer:**
$$
x =\,4\ \pm\ \sqrt{11}
$$
$$ x = 4 \pm \sqrt{11} $$

Solve the following quadratic
function by completing the square

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Algebra Questions