Question

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

Answer 1

Answer:

Step-by-step explanation:

x²+6x = 18

coefficient of the x term:  6

divide it in half:  3

square it:  3²

add 3² to both sides to complete the square and keep the equation balanced:

x²+6x+3² = 18+3²

(x+3)² = 27

x+3 = ±√27 = ±3√3

x = -3±3√3

Answer 2

Step-by-step explanation:

Use formula

$(\frac{b}{2} ) {}^{2}$

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

$x {}^{2} + 6x = 18$

$( \frac{6}{2} ) {}^{2}$

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

$x + 3 = \sqrt{27}$

Subtract 3 from both sides

$x = \sqrt{27} - 3$

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

$\sqrt{27} - 3$

or

$- ( \sqrt{27} ) - 3$