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 form

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


   



Question 51296: 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.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+-+4x+-+5+=+0
(a)
%28x+-+5%29%2A%28x+%2B+1%29
x+=+5
x+=+-1
(b)
x%5E2+-+4x+-+5+=+0
x%5E2+-+4x+=+5
To complete the square, divide the coefficient
of x by 2 and square the result. Use this as the constant term
You must add it to the other side also to keep the equation
balenced
x%5E2+-4x+%2B+4+=+5+%2B+4
%28x+-+2%29%5E2+=+9
Take the square root of both sides
Note that there are both negative and positive roots
%2B%28x+-+2%29+=+3
-%28x+-+2%29+=+3
x+=+5
x+=+-1
(c)
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A%28-5%29+%29%29%2F%282%2A1%29+
x+=+%284+%2B-+sqrt%28+16+%2B+20+%29%29%2F+2+
x+=+%284+%2B-+sqrt%28+36+%29%29%2F+2+
x+=+%284+%2B-+6%29+%2F+2
x+=+%284+%2B+6%29+%2F+2
x+=+5
x+=+%284+-+6%29+%2F+2
x+=+-1