About Completing the Square:
We can solve any quadratic equation using a process known as completing the square. This process creates a perfect square trinomial on one side of the equation, with a constant on the other. We then factor using our special factoring formulas and solve the equation using the square root property.
Test Objectives
- Demonstrate the ability to form a perfect square trinomial by completing the square
- Demonstrate the ability to factor a perfect square trinomial into the square of a binomial
- Demonstrate the ability to solve a quadratic equation of the form: (x + a)2 = k
#1:
Instructions: Solve each equation by completing the square.
a) $$4p^2 - 16=6p$$
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#2:
Instructions: Solve each equation by completing the square.
a) $$-k^2-15k=14$$
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#3:
Instructions: Solve each equation by completing the square.
a) $$8m^2 + 9m - 72=5m$$
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#4:
Instructions: Solve each equation by completing the square.
a) $$19a=-4a^2 + 93$$
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#5:
Instructions: Solve each equation by completing the square.
a) $$7p^2 + 21p=-9$$
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Written Solutions:
#1:
Solutions:
a) $$p=\frac{\pm\sqrt{73}+ 3}{4}$$
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#2:
Solutions:
a) $$k=-1$$ or $$k=-14$$
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#3:
Solutions:
a) $$m=\frac{\pm \sqrt{145}- 1}{4}$$
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#4:
Solutions:
a) $$a=3$$ or $$a=-\frac{31}{4}$$
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#5:
Solutions:
a) $$p=\frac{\pm 3\sqrt{21}- 21}{14}$$
