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
Step-by-step explanation:
Use formula
[tex] (\frac{b}{2} ) {}^{2} [/tex]
To add a third new term and factor to find the answer. Example
[tex]x {}^{2} + 6x = 18[/tex]
[tex]( \frac{6}{2} ) {}^{2} [/tex]
Which equal 9. so our equation look like
[tex] {x}^{2} + 6x + 9 = 18 + 9[/tex]
The only number that multiply to 9 and add up to 6 is 3. So we write our equation like this.
[tex](x + 3) {}^{2} = 27[/tex]
Take the sqr root of both sides
[tex]x + 3 = \sqrt{27} [/tex]
Subtract 3 from both sides
[tex]x = \sqrt{27} - 3[/tex]
Since a sqr root of a number can be positive or negative, the answer is
[tex] \sqrt{27} - 3[/tex]
or
[tex] - ( \sqrt{27} ) - 3[/tex]
