Final answer:
To solve the quadratic equation x²+6x=18 by completing the square, rearrange the equation, add the square of half the coefficient of x to both sides, rewrite the left side as a perfect square, take the square root, and solve for x.
Step-by-step explanation:
To solve the quadratic equation x²+6x=18 by completing the square, we need to rearrange the equation to have the form (x + a)² = b, where 'a' and 'b' are constants.
In this case, we add the square of half the coefficient of x to both sides of the equation:
x² + 6x + (6/2)² = 18 + (6/2)²
x² + 6x + 9 = 27
Now, we can rewrite the left side of the equation as a perfect square:
(x + 3)² = 27
Taking the square root of both sides, we get:
x + 3 = ±√27
Simplifying further, we have:
x + 3 = ±3√3
Finally, we can solve for x by subtracting 3 from both sides:
x = -3 ± 3√3
Learn more about Solving quadratic equations by completing the square