SOLUTION: using the quadratic equation x² - 4x - 5 = 0, perform the following task: solve by factoring, solve by completing the square, and solve using the quadratic formula

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: using the quadratic equation x² - 4x - 5 = 0, perform the following task: solve by factoring, solve by completing the square, and solve using the quadratic formula      Log On


   



Question 51693: using the quadratic equation x² - 4x - 5 = 0,
perform the following task:
solve by factoring,
solve by completing the square,
and solve using the quadratic formula

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
using the quadratic equation x² - 4x - 5 = 0, 
perform the following task: 
solve by factoring,
solve by completing the square,
and solve using the quadratic formula

-------------------------------

By factoring:

x² - 4x - 5 = 0

(x - 5)(x + 1) = 0

Setting x - 5 = 0 gives x = 5
Setting x + 1 = 0 gives x = -1

-------------------------------

By completing the square:

Get the constant term, -5, off the left side by
adding +5 to both sides of the equation:

                          x² - 4x = 5

To the side, multiply the coefficient of x, which is
-4, by 1/2, getting -2.  Then square this -2. getting,
(-2)² or 4.  Now add 4 to both sides:

                      x² - 4x + 4 = 5 + 4 

The left side will factor as (x - 2)(x - 2) or (x - 2)².
We combine the numbers on the right as 9

                         (x - 2)² = 9

Now we take square roots of both sides.

                            x - 2 = ±3

                                x = 2 ± 3

Using the +,  x = 2 + 3, or x = 5

Using the -, x = 2 - 3, or x = -1

-----------------------------------

By the quadratic formula:

        x² - 4x - 5 = 0

The quadratic formula is:

       ax² + bx + c = 0 has solutions:
                  ______ 
            -b ± Öb²-4ac
        x = —————————————
                2a 

In this cases a = 1; b = -4; c = -5

                      ______________
             -(-4) ± Ö(-4)²-4(1)(-5)
        x = ——————————————————————————
                     2(1) 
                  _____ 
             4 ± Ö16+20
        x = ————————————————
                  2

                   __ 
              4 ± Ö36
        x = ————————————————
                  2

                    
              4 ± 6
        x = —————————
                2

Using the +,  

              4 + 6
        x = —————————
                2


             10
        x = ————
              2         

        x = 5 
       
Using the -,  

              4 - 6
        x = —————————
                2


             -2
        x = ————
              2         

        x = -1 

Edwin