Question

Determine the next step for solving the quadratic equation by completing the square. 0 = –2x2 + 2x + 3 –3 = –2x2 + 2x –3 = –2(x2 – x) –3 + = –2(x2 – x + ) = –2(x – )2 = (x – )2 The two solutions are

Answer 1

We have that
0 = –2x²+ 2x + 3

Group terms that contain the same variable, and move the constant to the opposite side of the equation

(–2x²+ 2x)=-3

Factor the leading coefficient 

-2*(x²-x)=-3

Complete the square. Remember to balance the equation by adding the same constants to each side

-2*(x²-x+0.25)=-3-0.50

Rewrite as perfect squares

-2*(x-0.5)²=-3.50

(x-0.5)²=-3.50/-2

(x-0.5)²=1.75------> square root both sides

(+/-)(x-0.5)=√7/2

(+)(x-0.5)=√7/2----> (√7/2)+0.5----> x=1.823

(-)(x-0.5)=√5/2-----> x=0.5-(√7/2)----> x=-0.823

the solutions are

x=1.823

x=-0.823

Answer 2

Answer:

-1/2, 1/4, 1/2

Step-by-step explanation: