Question

X^2 + 4x - 7x = 0
GIVE YOUR ANSWER TO THE CORRECT 2 DECIMAL PLACES

Answer 1

x = -5.32, x = 1.32

Explanation:

Ok. So to use the Complete the Square method, you divide the middle value by 2 and then square the number you get. This will give:

`(x^(2) + 4x + ((4)/(2)) ^2) - ((4)/(2)) ^2 -7 = 0`

`(x^(2) + 4x + 4) - 4 -7 = 0`

`(x^(2) + 4x + 4) - 11 = 0`

`(x^(2) + 4x + 4) = 11` (now factor the left side)

`(x + 2)(x + 2) = 11`

`(x + 2)^(2) = 11` (now square root both sides)

`\sqrt{(x + 2)^(2)} = √(11)`

`x + 2 = √(11)`

`x = - 2 +/- √(11)` (+/- = plus or minus)

x = -5.32, x = 1.32

Answer 2

x ≈ - 5.32, x ≈ 1.32

Explanation:

x² + 4x - 7 = 0 ( add 7 to both sides )

x² + 4x = 7

To complete the square

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

x² + 2(2)x + 4 = 7 + 4

(x + 2)² = 11 ( take the square root of both sides )

x + 2 = ±
`√(11)` ( subtract 2 from both sides )

x = - 2 ±
`√(11)`

Thus

x = - 2 -
`√(11)` ≈ - 5.32 ( to 2 dec. places )

x = - 2 +
`√(11)` ≈ 1.32 ( to 2 dec. places )