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Solving to Complete the Square Solutions

You can use the Virtual Manipulatives to create perfect square trinomials when the answers are integers. The Virutal Manipulatives provide a great visual for quadratic trinomials.

Remember: Squares have equal length and width.

Use the Virtual Manipulatives to build the perfect square trinomial: $x^{2} + 6 x + 9 .$
Hint: The length and width are $x + 3 .$

Write the factored answer as a binomial squared.

${(x + 3)}^{2}$

What is the value of c (the units blocks) that will make the figure and the expression $x^{2} + 12 x + c$ a square?

What is the value of b that will make this figure a square?

8x or –8x

Write the expression for the perfect square trinomial.

$x^{2} + 8 x + 16$
or
$x^{2} - 8 x + 16$

Write the expression for the perfect trinomial square including the missing term.

$4 x^{2} - 4 x + 1$

Write the perfect trinomial square as a binomial squared.

${(2 x - 1)}^{2}$

For problems 5–8, use the Virtual Manipulatives to create perfect trinomial squares. Write the perfect square trinomial and the factored trinomial as a binomial squared.

$x^{2} - 10 x + c$

$x^{2} - 10 x + 25 = {(x - 5)}^{2}$

$a x^{2} + 12 x + 4$

$9 x^{2} + 12 x + 4 = {(3 x + 2)}^{2}$

$x^{2} - b x + 25$

$x^{2} - 10 x + 25 = {(x - 5)}^{2}$

$x^{2} - 8 x + c$

$x^{2} - 8 x + 16 = {(x - 4)}^{2}$