Answer:
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
