Question

Solve by completing the square x²+8x=13

Answer 1

x = - 4 ±
`√(29)`

Explanation:

the coefficient of the x² term is 1 as required

to complete the square

add (half the coefficient of the x-term )² to both sides

x² +2(4)x + 16 = 13 + 16

(x + 4)² = 29 ( take the square root of both sides )

x + 4 = ±
`√(29)` ← note plus or minus

subtract 4 from both sides

x = - 4 ±
`√(29)` ← exact solutions

Answer 2

Answer:
`\bold{x = -4\pm √(29)}`

Explanation:

Step 1: Create a perfect square: Add the value to both sides

x² + 8x + 16 = 13 + 16

↓ ↑ ↑

`(8)/(2) = (4)^2`

Step 2: Factor left side so it is a perfect square and simplify right side:

`(x + 4)^2 = 29`

Step 3: Take the square root of both sides

`x + 4 = \pm √(29)`

Step 4: Solve for x:

`x = -4\pm √(29)`