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