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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
Explain the following terms .
(1) Abiotic factors in an ecosystem
Abiotic factors are non living components of ecosystem.These include physical and chemical elements like temperature,light,water,soil,air quality and oxygen etc
Qasim
passive process of transport of low-molecular weight material according to its concentration gradient
AI-Robot
what is production?
Catherine
how did the oxygen help a human being
how did the nutrition help the plants
Biology is a branch of Natural science which deals/About living Organism.
evolutionary history and relationship of an organism or group of organisms
AI-Robot
cell is the smallest unit of the humanity biologically
Abraham
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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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