Question

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

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

Answer 1

Answer:

• The two solutions are:           $x=\frac{1}{2}+/-\frac{\sqrt{7} }{2}$

• The next and every step are below.

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:

$(x-1/2)=+/-\sqrt{\frac{7}{4}}\\ \\ x-1/2=+/-\frac{\sqrt{7} }{2}\\ \\ x=\frac{1}{2}+/-\frac{\sqrt{7} }{2}$