﻿ GreeneMath.com - Solving Quadratic Equations by Completing the Square Test
Completing the Square Test

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) $$4p^2 - 16 = 6p$$

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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:

Solution:

a) $$p = \frac{\pm\sqrt{73} + 3}{4}$$

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#2:

Solution:

a) $$k = -1$$ or $$k = -14$$

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#3:

Solution:

a) $$m = \frac{\pm \sqrt{145} - 1}{4}$$

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#4:

Solution:

a) $$a = 3$$ or $$a = -\frac{31}{4}$$

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#5:

Solution:

a) $$p = \frac{\pm 3\sqrt{21} - 21}{14}$$

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