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 equation.
$$a)\hspace{.2em}x^2 - 4x - 32=0$$
$$b)\hspace{.2em}x^2 - 4x - 60=0$$
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#2:
Instructions: solve each equation.
$$a)\hspace{.2em}x^2 - 10x - 36=0$$
$$b)\hspace{.2em}3x^2 + 6x - 70=-10$$
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#3:
Instructions: solve each equation.
$$a)\hspace{.2em}x^2 - 4x + 48=-5$$
$$b)\hspace{.2em}2x^2 + 4x + 4=10$$
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#4:
Instructions: solve each equation.
$$a)\hspace{.2em}4x^2 + 73=6 - 2x$$
$$b)\hspace{.2em}8x^2 - 10x + 5=-8x$$
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#5:
Instructions: solve each equation.
$$a)\hspace{.2em}69 - 17x=4x - 2x^2$$
$$b)\hspace{.2em}10x^2 - 4x=142$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}x=-4, 8$$
$$b)\hspace{.2em}x=-6, 10$$
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#2:
Solutions:
$$a)\hspace{.2em}x=5 \pm \sqrt{61}$$
$$b)\hspace{.2em}x=-1 \pm \sqrt{21}$$
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#3:
Solutions:
$$a)\hspace{.2em}x=2 \pm 7i$$
$$b)\hspace{.2em}x=-3, 1$$
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#4:
Solutions:
$$a)\hspace{.2em}x=\frac{-1 \pm i\sqrt{267}}{4}$$
$$b)\hspace{.2em}x=\frac{1 \pm i\sqrt{39}}{8}$$
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#5:
Solutions:
$$a)\hspace{.2em}x=\frac{21 \pm i\sqrt{111}}{4}$$
$$b)\hspace{.2em}x=\frac{1 \pm 2\sqrt{89}}{5}$$
