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

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

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

the answer is:

mean: 6

mad: 2.14