Question

Solve this quadratic equation by completing the square
x^2+6x=18

Answer 1

-8.20 (3sf) , 2.20 (3sf)

Explanation:

x2 + 6x = 18

halve the coefficient of x and square it, in this case it is ( 6 / 2 )2 which is 9)

x2 + 6x + 9 - 9 = 18

+ 9 on both sides,

( x + 3 )2 =27

ok now sq. root both sides

x + 3 = ±
`√(27\\)`

x + 3 = ± 5.196 (4 sf)

x = -8.20 (3 sf) or x = 2.20 (3sf)

Answer 2

( x + 3 )² - 27

Explanation:

x² + 6x = 18

→ Minus 18 from both sides to get a quadratic equation

x² + 6x - 18

⇒Completed square from is ( x + a )² + b

⇒The value of 'a' will always be half the 'b' value in the equation

ax² + bx + c

→( x + 3 )² + b

Expand out the equation to find 'b'

x² + 6x + 9

We have do something to get from 9 to - 18 which -27

So the answer is ( x + 3 )² -27