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) $$r= \pm 4$$
b) $$x= \pm \sqrt{15}$$
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#2:
Solutions:
a) $$x=5, 3$$
b) $$x=-7 \pm \sqrt{10}$$
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#3:
Solutions:
a) $$x=\frac{5}{2}, -\frac{7}{3}$$
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#4:
Solutions:
a) $$p=2, -\frac{19}{6}$$
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#5:
Solutions:
a) $$b=\frac{5 \pm i\sqrt{15}}{4}$$
