Answer:
The solutions of the equation are √3 - 1/2 and -√3 - 1/2
Step-by-step explanation:
* Lets revise how to make the completing square
- The form of the completing square is (x - h)² + k, where h , k
are constant
- The general form of the quadratic is x² + bx + c, where b , c
are constant
- To change the general form to the completing square form equate
them and find the constant h , k
* Now lets solve the problem
∵ x² + x = 11/4 ⇒ subtract 11/4 from both sides
∴ x² + x - 11/4 = 0
- Put the equation equal the form of the completing square
∵ x² + x - 11/4 = (x - h)² + k ⇒ solve the bracket power 2
∴ x² + x - 11/4 = x² - 2hx + h² + k
- Equate the like terms
∵ x = -2hx ⇒ divide both sides by x
∴ 1 = -2h ⇒ divide both sides by -2
∴ -1/2 = h
∴ the value of h = -1/2
∵ -11/4 = h² + k
- Substitute the value of h
∴ -11/4 = (-1/2)² + k
∴ -11/4 = 1/4 + k ⇒ subtract 1/4 from both sides
∴ -12/4 = k
∴ k = -3
∴ The value of k is -3
- Substitute the value of h and k in the completing square form
∴ (x - -1/2)² + (-3) = 0
∴ (x + 1/2)² - 3 = 0 ⇒ add 3 to both sides
∴ (x + 1/2)² = 3 ⇒ take square root for both sides
∴ x + 1/2 = √3 OR x + 1/2 = -√3
∵ x + 1/2 = √3 ⇒ subtract 1/2 from both sides
∴ x = √3 - 1/2
OR
∵ x + 1/2 = -√3 ⇒ subtract 1/2 from both sides
∴ x = -√3 - 1/2
* The solutions of the equation are √3 - 1/2 and -√3 - 1/2
