Question

Complete the square: x2 + 8x + 6 = 0

Answer 1

X2+8X+6=0

We add all the numbers together, and all the variables

X^2+8X+6=0

a = 1; b = 8; c = +6;

Δ = b2-4ac

Δ = 82-4·1·6

Δ = 40

The delta value is higher than zero, so the equation has two solutions

We use following formulas to calculate our solutions:

X1=−b−Δ√2aX2=−b+Δ√2a

The end solution:

Δ−−√=40−−√=4∗10−−−−−√=4√∗10−−√=210−−√

X1=−b−Δ√2a=−(8)−210√2∗1=−8−210√2

X2=−b+Δ√2a=−(8)+210√2∗1=−8+210√2

Explanation:

Answer 2

x = -4 ± √10

Explanation:

Step 1: Write quadratic

x² + 8x + 6 = 0

Step 2: Solve for x

1. Subtract 6 on both sides: x² + 8x = -6
2. Complete the Square: x² + 8x + 16 = -6 + 16
3. Complete the Square: (x + 4)² = 10
4. Square root both sides: x + 4 = ±√10
5. Subtract 4 on both sides: x = -4 ± √10