Exercise 3 Page 215

Completing the square is a method we can use to rewrite a part of quadratic equation as a perfect square trinomial. Then, we can factor this trinomial as the square of a binomial. This will lead us to an equation of the form shown below. (x+b)^2=d Here, b and d are real numbers. The advantage is that an equation of this form can be solved easier by first taking the square root of both sides and then isolating x. For example, consider the equation x^2 + 2x = 8. We can add 1 to both sides of the equation so that the left-hand side is a perfect square. x^2 + 2x = 8 ⇔ x^2 + 2x +1 = 9 Notice that x^2 + 2x +1 = (x+1)^2. x^2 + 2x +1 = 9 ⇔ (x+1)^2 = 9 The new equivalent equation we obtained can be solved in few steps.

(x+1)^2 = 9

SqrtEqn

sqrt(LHS)=sqrt(RHS)

x+1 = ± sqrt(9)

CalcRoot

Calculate root

x+1 = ± 3

SubEqn

LHS-3=RHS-3

x = ± 3 -1

Therefore, the solutions are x = -3 -1 = -4 and x = 3-1 = 2.