Question

Rewrite the equation by completing the square. 2x^2 - 11x + 14 = 0

Answer 1

To rewrite the equation 2x^2 - 11x + 14 = 0 by completing the square, follow these steps: move the constant term to the other side, take half of the x coefficient and square it, add that value to both sides, factor the perfect square trinomial, take the square root, and solve for x.

Step-by-step explanation:

To rewrite the equation by completing the square, follow these steps:

1. Move the constant term to the other side of the equation: 2x^2 - 11x = -14
2. Take half of the coefficient of the x term, square it, and add it to both sides of the equation:
   2x^2 - 11x + (-11/2)^2 = -14 + (-11/2)^2
   Simplify:
   2x^2 - 11x + 121/4 = -14 + 121/4
3. Factor the perfect square trinomial on the left side:
   (x - 11/2)^2 = (-56 + 121/4) / 4
4. Simplify:
   (x - 11/2)^2 = 65/4
5. Take the square root of both sides:
   x - 11/2 = ±√(65/4)
   Simplify:
   x - 11/2 = ±√65/2
6. Add 11/2 to both sides to solve for x:
   x = 11/2 ±√65/2