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

1 answer
Question:

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

Answers

Answer:The solutions of the equation are √3 - 1/2 and -√3 - 1/2Step-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 - 1/2OR∵ 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

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