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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> 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      Log On


   

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



x%5E2+-+18x+%2B+81=+34

x%5E2+-+18x+%2B+81-34=0
x%5E2+-+18x+%2B+47=0

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


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2-18%2Ax%2B47=0 ( notice a=1, b=-18, and c=47)





x+=+%28--18+%2B-+sqrt%28+%28-18%29%5E2-4%2A1%2A47+%29%29%2F%282%2A1%29 Plug in a=1, b=-18, and c=47




x+=+%2818+%2B-+sqrt%28+%28-18%29%5E2-4%2A1%2A47+%29%29%2F%282%2A1%29 Negate -18 to get 18




x+=+%2818+%2B-+sqrt%28+324-4%2A1%2A47+%29%29%2F%282%2A1%29 Square -18 to get 324 (note: remember when you square -18, you must square the negative as well. This is because %28-18%29%5E2=-18%2A-18=324.)




x+=+%2818+%2B-+sqrt%28+324%2B-188+%29%29%2F%282%2A1%29 Multiply -4%2A47%2A1 to get -188




x+=+%2818+%2B-+sqrt%28+136+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%2818+%2B-+2%2Asqrt%2834%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%2818+%2B-+2%2Asqrt%2834%29%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%2818+%2B+2%2Asqrt%2834%29%29%2F2 or x+=+%2818+-+2%2Asqrt%2834%29%29%2F2



Now break up the fraction



x=%2B18%2F2%2B2%2Asqrt%2834%29%2F2 or x=%2B18%2F2-2%2Asqrt%2834%29%2F2



Simplify



x=9%2Bsqrt%2834%29 or x=9-sqrt%2834%29



So the solutions are:

x=9%2Bsqrt%2834%29 or x=9-sqrt%2834%29





2.


t%5E2+-+4t+%2B+4=+25
t%5E2+-+4t+%2B+4-+25=0
t%5E2+-+4t+-+21=0
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2-4%2Ax-21=0 ( notice a=1, b=-4, and c=-21)





x+=+%28--4+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A-21+%29%29%2F%282%2A1%29 Plug in a=1, b=-4, and c=-21




x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A-21+%29%29%2F%282%2A1%29 Negate -4 to get 4




x+=+%284+%2B-+sqrt%28+16-4%2A1%2A-21+%29%29%2F%282%2A1%29 Square -4 to get 16 (note: remember when you square -4, you must square the negative as well. This is because %28-4%29%5E2=-4%2A-4=16.)




x+=+%284+%2B-+sqrt%28+16%2B84+%29%29%2F%282%2A1%29 Multiply -4%2A-21%2A1 to get 84




x+=+%284+%2B-+sqrt%28+100+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%284+%2B-+10%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%284+%2B-+10%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%284+%2B+10%29%2F2 or x+=+%284+-+10%29%2F2


Lets look at the first part:


x=%284+%2B+10%29%2F2


x=14%2F2 Add the terms in the numerator

x=7 Divide


So one answer is

x=7




Now lets look at the second part:


x=%284+-+10%29%2F2


x=-6%2F2 Subtract the terms in the numerator

x=-3 Divide


So another answer is

x=-3


So our solutions are:

x=7 or x=-3