Question

Complete the square to solve the equation below. X^2 +x=11/4

Answer 1

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