Question

Solve this quadratic equation by completing the square.

x^2 + 6x = 18

Answer 1

Explanation:

Use formula

`((b)/(2) ) {}^(2)`

To add a third new term and factor to find the answer. Example

`x {}^(2) + 6x = 18`

`( (6)/(2) ) {}^(2)`

Which equal 9. so our equation look like

`{x}^(2) + 6x + 9 = 18 + 9`

The only number that multiply to 9 and add up to 6 is 3. So we write our equation like this.

`(x + 3) {}^(2) = 27`

Take the sqr root of both sides

`x + 3 = √(27)`

Subtract 3 from both sides

`x = √(27) - 3`

Since a sqr root of a number can be positive or negative, the answer is

`√(27) - 3`

or

`- ( √(27) ) - 3`