Algebra Tiles Activity 1: Adding Integers

Method 2: In the equation ax 2 + bx +c = 0, if a is not a square, then divide the equation by a.bDivide the in half and arrange the x 2 + b x into the beginning of a square. Add as many zeroa apairs as needed to make a square. Combine the extra +1's and –1's together.!Solve 3p 2 – 6p – 2 = 0 ⇒ p 2 – 2p –!23 = 0 –!Rearrange23–233p 2 – 6p – 2 = 0 ⇒ p 2 – 2p –!Solve: 2x 2 – 5x = 3 ⇒!54!54=x 2 " 5 2 x = 3 2!3223 = 0, (p – 1)2 –!!= 4916 ,!54542516!53 = 0, p =!=!!321± 5 3! !25Notice that in this example we did not add a zero pair of +16 and – 25to the left side of the1625! !equation, but instead added + to both sides of the equation.162x 2 – 5x = 3 ⇒x 2 " 5! 2 x = 3 2 ,#x " 5 &% ($ 4'2+2516!x " 5 4 = ± 7 4 , x = 3, " 1 2 .Solve the following equations by completing the square.1. x 2 ! 2x – 3 = 0 !!!2. x 2 + 4x = – 2