Solve the equation by completing the square. round to the nearest hundredth if necessary. 2x^2-4x=5

x = 2.87 and -0.87

Step-by-step explanation:

Rewrite 2x^2-4x=5 to make it easier to apply "completing the square:"

2(x^2 - 2x             ) = 5/2

Then complete the square, putting all work inside parentheses:

1) the coefficient of the x term is -2.  Take half of that:  we get -1.

2) square this result; we get +1.

3) Add this square to x^2 - 2x, and then subtract it from the sum:

                                    x^2 - 2x + 1             - 1

4) Rewrite the original   2(x^2 - 2x             ) = 5/2 as:

                                        2(x^2 - 2x + 1  -  1 ) = 5.

Note that x^2 - 2x + 1 can be rewritten as the square of a binomial:  (x - 1)^2.

Then we have:                 2(x - 1)^2 - 2 = 5, or

                                          2(x - 1)^2 = 7, or

                                              (x - 1)^2 = 7/2

5.  Take the square root of both sides:

                                               x - 1 = ±√(7/2)

6.  Write out the two roots:  

x = 1 + √(7/2) and

x  = 1 - √(7/2)

To the nearest hundredth:

x = 2.87 and -0.87

a variable is any characteristics, number, or quantity that can be measured or counted. a variable may also be called a data item. hope i !