SOLUTION: 1) Using the quadratic equation x2 - 4x - 5 = 0, perform the following tasks: a) Solve by factoring. b) Solve by completing the square. c) Solve by using the quadratic

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 1) Using the quadratic equation x2 - 4x - 5 = 0, perform the following tasks: a) Solve by factoring. b) Solve by completing the square. c) Solve by using the quadratic       Log On


   

Question 41701: 1) Using the quadratic equation x2 - 4x - 5 = 0, perform the following tasks:
a) Solve by factoring.
b) Solve by completing the square.

c) Solve by using the quadratic formula.

Thank you for the help in advance.
textbook info.
ISBN 0-321-27908-5
TITLE
COLLEGE ALGEBRA BY GARY ROCKSWOLD
3RD EDITION
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
FACTORIZATION METHOD
x%5E2+-+4x+-+5+=+0
or x%5E2+-+5x+%2B+x+-+5+=+0
or x%28x+-+5%29+%2B+1%28x+-+5%29+=+0
or %28x+-+5%29%28x+%2B+1%29+=+0
Therefore, either (x - 5) = 0 i.e. x = 5 or (x + 1) = 0 i.e. x = -1.



COMPLETING THE SQUARE METHOD
The equation x%5E2+-+4x+-+5+=+0 can also be written as
%28x%5E2+-+2%2Ax%2A2+%2B+2%5E2%29+-+9+=+0
%28x+-+2%29%5E2+=+9+=+3%5E2
Square-rooting both sides we have
either %28x+-+2%29+=+3 or %28x+-+2%29+=+-3
i.e. either x = 5 or x = -1.



QUADRATIC FORMULA METHOD
The formula, developed by Sreedharacharya, for solving quadratic equation ax%5E2+%2B+bx+%2B+c+=+0 is
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+.
Comparing with the standard quadratic equation, here a = 1, b = -4, c = -5.
Substituting these values in the formula we obtain
x+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A%28-5%29+%29%29%2F%282%2A1%29+
or x+=+%284+%2B-+sqrt%2816%2B20%29%29%2F2+
or x+=+%284+%2B-+sqrt%2836%29%29%2F2+
or x+=+%284+%2B-+6%29%2F2+
or x+=+2+%2B-+3+
So either x = 5 or x = -1.