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# Math.....question

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Portia solved the quadratic equation $$x^2+(2\sqrt3)x+1=0$$  by completing the square. In the process, she came up with the equivalent equation $$(x+r)^2 = s,$$ where $$r$$ $$s$$ and  are constants.

What is $$s$$?

tertre  Mar 11, 2017

#2
+76808
+5

x^2 + 2sqrt(3)x + 1  = 0

x^2 + 2sqrt(3)x  = - 1

Take (1/2) of 2sqrt(3)  = sqrt(3)....square this = 3   add to both sides

x^2 + 2sqrt(3)x + 3 =  -1 + 3      simpify and factor

(x  + sqrt(3) )^2   =    2

r =  sqrt(3), s = 2

CPhill  Mar 11, 2017
Sort:

#1
+1156
0

Where is says " r s and are constants", it's actually " r and s are constants

tertre  Mar 11, 2017
#2
+76808
+5

x^2 + 2sqrt(3)x + 1  = 0

x^2 + 2sqrt(3)x  = - 1

Take (1/2) of 2sqrt(3)  = sqrt(3)....square this = 3   add to both sides

x^2 + 2sqrt(3)x + 3 =  -1 + 3      simpify and factor

(x  + sqrt(3) )^2   =    2

r =  sqrt(3), s = 2

CPhill  Mar 11, 2017
#3
+1156
+5

Thanks so much!

tertre  Mar 11, 2017

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