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- Elementary algebra
- Quadratic equations
- Solving quadratic equations
The constant must be the square of one half the coefficient of
Since the coefficient of
is 3, we have
The constant is
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The method of completing the square
Now, with these observations, we can describe the method of completing the square.
The method of completing the square
- Write the equation so that the constant term appears on the right side of equation.
- If the leading coefficient is different from 1, divide each term of the equation by that coefficient.
- Take one half of the coefficient of the linear term, square it, then
add it to
both sides of the equation.
- The trinomial on the left is now a perfect square trinomial and can be factored as
The first term in the parentheses is the square root of the quadratic term. The last term in the parentheses is one-half the coefficient of the linear term.
- Solve this equation by extraction of roots.
Sample set a
Solve the following equations.
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Since we know that the square of any number is positive, this equation has no real number solution.
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Calculator problem. Solve
Round each solution to the nearest tenth.
- We will first compute the value of the square root.
Press the key that places this value into memory.
- For
Rounding to tenths, we get
- For
Rounding to tenths, we get
Thus,
and
to the nearest tenth.
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Practice set a
Solve each of the following quadratic equations using the method of completing the square.
Exercises
For the following problems, solve the equations by completing the square.
calculator problems
For the following problems, round each solution to the nearest hundredth.
Exercises for review
Questions & Answers
evolutionary history and relationship of an organism or group of organisms
AI-Robot
the study of living organisms and their interactions with one another and their environments
AI-Robot
HOW CAN MAN ORGAN FUNCTION
the diagram of the digestive system
allimentary cannel
Ogenrwot
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
Genetics is the study of heredity
Misack
how does twins formed?
Misack
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
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Source:
OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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