Solve each equation by completing the square: 2 x 2 + x = 8

Given equation: 2 x 2 + x = 8 The equation cannot be factorised. Now, 2 x 2 + x = 8 ⇒ x 2 + x 2 = 4 [dividing both sides by 2 ] ⇒ x 2 + 2 × x × 1 4 + 1 4 2 - 1 4 2 = 4 ⇒ x + 1 4 2 = 4 + 1 4 2 [Adding 1 4 2 to both sides] ⇒ x + 1 4 2 = 4 + 1 16 ⇒ x + 1 4 2 = 65 16 ⇒ x + 1 4 = ± 65 16 [Taking square root of both sides] ⇒ x = - 1 4 ± 8 . 06225 . . . 4 ⇒ x = - 9 . 06225 . . . 4 or 7 . 06225 . . . 4 ⇒ x = - 2 . 2655 . . . . or 1 . 7655 . . . [Solving for both values] ⇒ x = - 2 . 27 or 1 . 77 [Rounding the value up to 2 decimal places] The solution of x is - 2 . 27 or 1 . 77 .

Solve each equation by completing the square: x - 5 = 2 x

Given equation: x - 5 = 2 x The equation cannot be factorised. Now, x - 5 = 2 x ⇒ x 2 - 5 x = 2 ⇒ x 2 - 2 × x × 5 2 + 5 2 2 - 5 2 2 = 2 [Completing the square by writing x 2 - 5 x in the form of x + a 2 + b and getting - 5 2 as half of - 5 ] ⇒ x - 5 2 2 - 25 4 = 2 ⇒ x - 5 2 2 = 2 + 25 4 [Adding 25 4 to both sides] ⇒ x - 5 2 2 = 33 4 ⇒ x - 5 2 = ± 33 4 [Taking square root of both sides] ⇒ x = 5 2 ± 5 . 74456 . . . 2 ⇒ x = 10 . 74456 . . . 2 or - 0 . 74456 2 ⇒ x = 5 . 3722 . . . . . or - 0 . 37228 . . . [Solving for both options] ⇒ x = 5 . 37 or - 0 . 37 [Rounding the solution up to 2 decimal places] The solution of x is 5 . 37 or - 0 . 37

E M B I B E

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Algebra>Chapter 14 - Further Solving of Equations and Inequalities>Exercise 14.8

Karen Morrison and Nick Hamshaw Solutions for Exercise 8: Exercise 14.8

Author:Karen Morrison & Nick Hamshaw

Karen Morrison Mathematics Solutions for Exercise - Karen Morrison and Nick Hamshaw Solutions for Exercise 8: Exercise 14.8

Attempt the practice questions from Exercise 8: Exercise 14.8 with hints and solutions to strengthen your understanding. Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition solutions are prepared by Experienced Embibe Experts.