Question

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

Answer 1

To complete the square of the quadratic equation
`2x^(2)-11x+14=0`, the steps are: divide by 2, move the constant term, add the squared value of half the coefficient of x, and simplify. The result is (x - 11/4)^2 = 27/16.

Step-by-step explanation:

To rewrite the equation
`2x^2-11x+14=0` by completing the square, you can follow these steps:

1. Divide the entire equation by 2 to make the coefficient of
   `x^2` equal to 1.
2. Move the constant term (14) to the right side of the equation.
3. Take half of the coefficient of x (in this case, -11/2) and square it.
4. Add the squared value (121/4) to both sides of the equation.
5. Write the left side of the equation as a perfect square and simplify the right side.

The rewritten equation is -
`(x - 11/4)^2`

= 27/16.

Answer 2

2x^2 - 11x + 14 can be rewritten by completing the square as:

2(x - 5/2)^2 + 4 = 0

Step-by-step explanation:

Move the constant term to the right side:

2x^2 - 11x = -14

Divide both sides by 2 (optional but simplifies the process):

x^2 - 5.5x = -7

Find half of the coefficient of the x term:

Half of -5.5 is -2.75.

Square that value and add it to both sides of the equation:

(x^2 - 5.5x) + (-2.75)^2 = -7 + (-2.75)^2

Rewrite the left side as a squared term:

(x - 2.75)^2 = 5.25 = 0.75^2 + 4.5^2

Therefore, the equation becomes:

2(x - 5/2)^2 + 4 = 0

This form reveals that the original equation can be represented by a squared term plus a constant, which is a characteristic of a completed square.