For quadratic equations that cannot be solved by factorising, we use a method which can solve ALL quadratic equations called completing the square.Completing the square comes from considering the special formulas that we met in square of a sum and square of a difference earlier:(x + y)2 = x2 + 2xy + y2 (Square of a sum)(x − y)2 = x2 − 2xy + y2 (Square of a difference)To find the roots of a quadratic equation in the form:ax2 + bx + c = 0,follow these steps:(i) If a does not equal 1, divide each side bya (so that the coefficient of the x2 is 1).(ii) Rewrite the equation with the constantterm on the right side.(iii) Complete the square by adding the square of one-half of the coefficient of x to both sides.(iv) Write the left side as a square and simplify the right side.(v) Equate and solve.Example 1Find the roots of x2 + 10x − 4 = 0 using completing the square method.answer---Step (i) a = 1 [no action necessary in this example]Step (ii) Rewrite the equation with the constant term on the right side.x2 + 10x = 4Step (iii) Complete the square by adding the square of one-half of the coefficient of x to both sides. In this case:x2 + 10x + 25 = 4 + 25x2 + 10x + 25 = 29Step (iv) Write the left side as a square:(x + 5)2 = 29Step (v) Equate and solve

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