Solve the equation by completing the square, x^2 + 5x-5=0

Question

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Answer 1

(x^2 + 5x     )  - 5 = 0

 

Divide 5 by 2 and square it...  

 

(5/2)^2 = 25/4

 

 

Add 25/4 to both sides:

(x^2 + 5x + 25/4) - 5 = 0 + 25/4

 

Factor:

 

(x + 5/2)^2 - 5 = 25/4

 

Add 5 or (20/4) to both sides:

 

(x + 5/2)^2 = (25/4) + (20/4)

 

(x + 5/2)^2 = 45/4

 

Take the square root of both sides:

 

x + 5/2 = +/- sqrt(45)/sqrt(4)

 

x + 5/2 = +/- 3 sqrt(5)/2

 

Add -5/2 to both sides:

 

x = -5/2 +/- 3√5/2

 

 

Quadratic:

 

-5 +/- sqrt(25 - 4(1)(-5))

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

             2(1)

 

-5 +/- sqrt(45)

----------------      Check.

        2