Question

Determine the next step for solving the quadratic equation by completing the square

0= -2x^2 + 2x + 3

Answer 1

• The two solutions are:
  `x=(1)/(2)+/-(√(7) )/(2)`

• The next and every step are below.

Step-by-step explanation:

1.
`-3=-2x^2+2x` : Given (addition property / add - 3 to both sides)

2.
`-3 = - 2(x^2-x)` : Given (commom factor - 2)

3.
`-3-1/2=-2(x^2-x+1/4)`

To obtain the perfect square it was added the square of half of the coefficient of x: (1/2)² = 1/4, inside the parenthesis.

Since, the terms inside the parentthesis are multiplied by - 2, you have to add - 2 (1/4) = - 1/2 to the left side of the equation.

4. Now, you have that the trinomial x² - x + 1/4 is a square perfect trinomial which is factored as (x - 1/2)² and get the expression:

`-7/2=-2(x-1/2)^2`

5. Divide both sides by - 2 to get the next expression:

`-7/4=(x-1/2)^2`

6. The last step is to extract squere root from both sides of the equality:

`(x-1/2)=+/-\sqrt{(7)/(4)}\\ \\ x-1/2=+/-(√(7) )/(2)\\ \\ x=(1)/(2)+/-(√(7) )/(2)`