SOLUTION: 1) Using the quadratic equation x2 - 4x - 5 = 0, perform the following tasks: a) Solve by factoring. Answer: Show work in this space. b) Solve by completing the squ

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 1) Using the quadratic equation x2 - 4x - 5 = 0, perform the following tasks: a) Solve by factoring. Answer: Show work in this space. b) Solve by completing the squ      Log On


   

Question 53228: 1) Using the quadratic equation x2 - 4x - 5 = 0, perform the following tasks:
a) Solve by factoring.
Answer:
Show work in this space.


b) Solve by completing the square.
Answer:
Show work in this space.


c) Solve by using the quadratic formula.
Answer:
Show work in this space


Thank You in Advance
Found 2 solutions by funmath, venugopalramana:
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
a)Facotring:
Two nunmbers that multiply together to get -5, but add together to get -4 are -5 and 1, so
x%5E2-4x-5=0
%28x-5%29%28x%2B1%29=0
Set both parenthesis = to 0 and solve for x.
x-5=0
x-5+5=0+5
x=5
and
x+1=0
x+1-1=0-1
x=-1
x={-1,5}
--------------------------------------------
b)Completing the square.
First move the things without x's to the other side of the equal sign within the rules of algebra:
x%5E2-4x-5%2B5=0%2B5
x%5E2-4x=5
Take 1/2 od the coefficient of x and square it and add it to both sides of the equation:
x%5E2-4x%2B%28-4%2F2%29%5E2=5%2B%28-4%2F2%29%5E2
x%5E2-4x%2B%28-2%29%5E2=5%2B%28-2%29%5E2
Factor the left side and simplify the right:
%28x-2%29%5E2=5%2B4
%28x-2%29%5E2=9
Take the square root of both sides:
%28sqrt%28x-2%29%29%5E2=%2B-sqrt%289%29
(x-2)=+-3
Solve for x twice:
x-2=-3
x-2+2=-3+2
x=-1
x-2=3
x-2+2=3+2
x=5
x={-1,5}
------------------------------------------------------
c) Quadratic Formula:
When
ax%5E2%2Bbx%2Bc=0
x=%28-b%2B-sqrt%28b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29
x%5E2-4x-5=0
a=1, b=-4, c=-5
x=%28-%28-4%29%2B-sqrt%28%28-4%29%5E2-4%281%29%28-5%29%29%29%2F%282%2A1%29
x=%284%2B-sqrt%2816%2B20%29%29%2F2
x=%284%2B-sqrt%2836%29%29%2F2
x=(4-6)/2
x=-2/2
x=-1
x=(4+6)/2
x=10/2
x=5
x={-1,5}

Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
1) Using the quadratic equation x2 - 4x - 5 = 0, perform the following tasks:
a) Solve by factoring.
Answer:
Show work in this space.
X^2-4X-5=X^2-5X+X-5=X(X-5)+1(X-5)=(X-5)(X+1)=0
X=5.....OR.....-1
b) Solve by completing the square.
Answer:
Show work in this space.
X^2-2(X)(2)+2^2-2^2-5=0
(X-2)^2-9=0
(X-2)^2=9
X-2=3..............OR.............X-2=-3
X=5................OR.............X=-1
c) Solve by using the quadratic formula.
Answer:
Show work in this space
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%284+%2B-+sqrt%28+16-4%2A1%2A%28-5%29+%29%29%2F%282%2A1%29+
x+=+%284+%2B-+sqrt%28+36+%29%29%2F%282%29+
x=(4+6)/2 = 5 .......OR........(4-6)/2=-1