### About Completing the Square:

We previously learned how to solve quadratic equations by factoring. In many cases, we must utilize a different method. When this occurs, we can turn to a method known as completing the square. This method creates a perfect square trinomial on one side and sets it equal to a constant on the other. We can then solve using the square root property.

Test Objectives

- Demonstrate the ability to use the square root property
- Demonstrate the ability to solve a quadratic equation by completing the square
- Demonstrate the ability to solve a quadratic equation with a complex solution

#1:

Instructions: Solve each using the square root property.

a) $$5r^2 - 8=72$$

b) $$3x^2 - 4=41$$

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#2:

Instructions: Solve each using the square root property.

a) $$(x - 4)^2 - 7=-6$$

b) $$(x + 7)^2 + 2=12$$

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#3:

Instructions: Solve each by completing the square.

a) $$13x^2 - x - 35=7x^2$$

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#4:

Instructions: Solve each by completing the square.

a) $$12p^2 - 76=-14p$$

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#5:

Instructions: Solve each by completing the square.

a) $$-b^2 - 5b +5=-3b^2$$

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Written Solutions:

#1:

Solutions:

a) $$r=4 \hspace{.5em}or \hspace{.5em}r=-4$$

b) $$x=\sqrt{15}\hspace{.5em}or \hspace{.5em}x=-\sqrt{15}$$

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#2:

Solutions:

a) $$x=5 \hspace{.5em}or \hspace{.5em}x=3$$

b) $$x=-7 + \sqrt{10}\hspace{.5em}or \hspace{.5em}x=-7 - \sqrt{10}$$

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#3:

Solutions:

a) $$x=\frac{5}{2}\hspace{.5em}or \hspace{.5em}x=-\frac{7}{3}$$

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#4:

Solutions:

a) $$p=2 \hspace{.5em}or \hspace{.5em}p=-\frac{19}{6}$$

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#5:

Solutions:

a) $$b=\frac{5 + i\sqrt{15}}{4}\hspace{.5em}or \hspace{.5em}b=\frac{5 - i\sqrt{15}}{4}$$