SOLUTION: the quadratic equation exercises that are attached to this note and demonstrate how your quadratic equation is solved by the Factoring Method. Explain your steps. Demonstrate how y

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Question 397228: the quadratic equation exercises that are attached to this note and demonstrate how your quadratic equation is solved by the Factoring Method. Explain your steps. Demonstrate how your quadratic equation expression is solved by the Square Root Property. Explain your steps. Two quadratic equations (similar to the ones you chose to explain above) for your classmates to solve using the algorithms to work with quadratic equations.
12.
16.

Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!
1.








Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic





the general solution using the quadratic equation is:







So lets solve ( notice , , and )





Plug in a=1, b=-18, and c=47




Negate -18 to get 18




Square -18 to get 324 (note: remember when you square -18, you must square the negative as well. This is because .)




Multiply to get




Combine like terms in the radicand (everything under the square root)




Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


or



Now break up the fraction



or



Simplify



or



So the solutions are:

or





2.





Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic





the general solution using the quadratic equation is:







So lets solve ( notice , , and )





Plug in a=1, b=-4, and c=-21




Negate -4 to get 4




Square -4 to get 16 (note: remember when you square -4, you must square the negative as well. This is because .)




Multiply to get




Combine like terms in the radicand (everything under the square root)




Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


or


Lets look at the first part:





Add the terms in the numerator

Divide


So one answer is






Now lets look at the second part:





Subtract the terms in the numerator

Divide


So another answer is




So our solutions are:

or











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