Exercise 148 Page 357

Nobody is correct. George tried using the Zero Product Property. However, Jeffrey correctly identified the error in George's ways. In order to use the Zero Product Property, one of the sides has to equal zero, which is not the case for the given equation. (2x-1)(x+3)= 4 ← not zero But to set the factors equal to 4 and solving for x will not help either. In order for the solved x to be a solution, the other factor must equal 1 for the solution. This is not necessarily the case. Let's set each factor equal to 4 and solve for x. x+3=4 &⇔ x=1 2x-1=4 &⇔ x=5/2 Let's test these solutions in the original equation.

The first solution was correct. Let's try the second solution.

The second solution was not a solution at all. To solve the equation correctly, we must rewrite the equation so that the right-hand side equals 0.

Now we can solve the equation by, for example, completing the square. Notice that in order to complete the square, x^2 has to have a coefficient of 1. Therefore, we have to start by dividing both sides of the equation by 2.