Question

SoIve the quadratic equation by completing the square. x²+18x+66=0

Answer 1

To solve the quadratic equation x²+18x+66=0 by completing the square, reorder the equation, complete the square, factor the perfect square, take the square root, and write the solutions.

Step-by-step explanation:

To solve the quadratic equation x²+18x+66=0 by completing the square:

1. Reorder the equation so that the constant term (66) is on one side and the variable terms (x² and 18x) are on the other side.
2. Complete the square by adding the square of half the coefficient of x to both sides of the equation.
3. Factor the perfect square on the left side of the equation and simplify.
4. Take the square root of both sides to solve for x.
5. Finally, write the two solutions for x.

Therefore, the solutions for the quadratic equation x²+18x+66=0 are x=-3 and x=-11.