Completing the Square with Algebra Tiles

A hands on approach to completing the squareCompleting the Square with Algebra TilesCompleting the Square2Algebra tiles can be used to complete the squareUse tiles and frame to represent problem. The expression should form a square array inside the frame.The square factors will form the dimensionsBe prepared to use zero pairs of constants to complete the square

Rewrite as a binomial squared3x2 + 4x Determine and model the dimensions of the squareModel the expressionArrange the tiles so they start to form a square.x2 + 4x+4 = Determine how many 1s you have to add to make it a squareEx: Complete the square for

Rewrite as a binomial squared4x2 6x Determine and model the dimensions of the squareModel the expressionArrange the tiles so they start to form a square.x2 6x+9 = Determine how many 1s you have to add to make it a squareEx: Complete the square for

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PatternsWhat patterns have you noticed? What did you do with the x terms in order to make a square?What pattern did you see for adding your constant term?How is your constant term related to your middle term?Solving Equations by completing the squareWe will complete the square on one side of the equation.Remember that whatever we add to one side of the equation, we must add to the other.Then re-write our perfect square trinomial as the sum/difference of a binomial.Use the Square Root Method to solve for x!Ex: Solve

First, model the equation.Next, arrange the left side to form a squareComplete the square by adding 1sAdd to both sidesRewrite each side

Write as the sum of a binomial

Take the square root of each side

Ex: Solve

First, model the equation.Next, arrange the left side to form a squareComplete the square by adding 1sAdd to both sidesRewrite each side

Write as the sum of a binomial

Take the square root of each side

You try