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Around 700AD the general solution for the quadratic equation, this time using numbers, was devised by a Hindu mathematician called Brahmagupta.
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*History of the Quadractic Formula Cond.*
It is known that the Egyptian wise men (engineers, scribes and priests) were aware of this shortcoming.
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*First Step*
The quadratic equation looks like this:
ax ² + bx + c = 0
A, B, C are coefficients in the quadratic equation.
Need to solve for ‘x’.
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*Second Step*
Example Equation: x ² 4 x 5 = 0
Substitute A=1, B= -4, C=-5
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*Third Step*
Solve Equation in this formula:
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*Fourth Step*
Plug in the A, B, C in the Quadratic Formula. A=1, B=-2, C=1
So for B plug in –2. For C plug in 1 and for A plug in 1.
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*Fifth Step*
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*Sixth Step*
Substitute the variables in the equation and solve what is under the radical first.
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*Seventh Step*
Depending on the problem, you will need two answers usually.
In this problem, you just need one answer since the number under the radical is 0.
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*Eighth Step*
The very last step you need to add the –2 (B variable) with the radical number and then divide by 2 in this case.
Since the variable (A) on the bottom was 1 then you would just divide by two.
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*Ninth Step*
You would multiply the 2 and variable A which would be 1 in this problem.
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*Tenth Step* *As you can see the two different steps at the end* Add and subtract to get the final two answers.
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*Eleventh Step* When you substitute a number for the variable B and it is a negative number it becomes a positive number. As shown in the example.
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*Twelfth Step*
A more complex quadratic problem- You simplify the 3 rd step in the example to the –3 + and – radical 5. The last step, simplify the 2 and –8 after by 2…leaving a –4 on the bottom.
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*Thirteenth Step*
Leaving the five under the radical and coming up with two answers 3+ radical 5 and 3 – radical 5.
These are some of the examples that will help to solve simple quadratic equations to the more complex ones.
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Works Cited
BBC - H2g2 - The History Behind The Quadratic Formula." BBC - Homepage . H2g2's Researchers, 13 Oct. 2004. Web. 11 Oct. 2010. <http://www.bbc.co.uk/dna/h2g2/A 2982567>.
"Quadratic Formula." Math Homework Help – Math