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
Completing the Square Test:
#1:
Instructions: Solve each equation by completing the square.
a) $$4p^2 - 16 = 6p$$
#2:
Instructions: Solve each equation by completing the square.
a) $$-k^2-15k = 14$$
#3:
Instructions: Solve each equation by completing the square.
a) $$8m^2 + 9m - 72 = 5m$$
#4:
Instructions: Solve each equation by completing the square.
a) $$19a = -4a^2 + 93$$
#5:
Instructions: Solve each equation by completing the square.
a) $$7p^2 + 21p = -9$$
Written Solutions:
Solution:
a) $$p = \frac{\pm\sqrt{73} + 3}{4}$$
Solution:
a) $$k = -1$$ or $$k = -14$$
Solution:
a) $$m = \frac{\pm \sqrt{145} - 1}{4}$$
Solution:
a) $$a = 3$$ or $$a = -\frac{31}{4}$$
Solution:
a) $$p = \frac{\pm 3\sqrt{21} - 21}{14}$$