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1.When solving a quadratic by completing the square, how do you keep the equation balanced?

2.  Given the equation 5x^2+10x+20=0  why do you divide all terms by five before completing the square? 

Guest Sep 18, 2018

Best Answer 

 #1
avatar+14592 
+2

Perform the same operation on BOTH sides of the equation .Always add the same amounts to BOTH sides of the equation. 

 

Divide by 5 to get leading coefficient of the x^2 term to equal '1'.....necessary for 'Completing theSquare' operation

 

5x^2  + 10x +20 = 0      DIvide both sides of the equation by '5'

x^2 + 2x + 4 = 0   re-arrange

x^2 + 2x = -4

 

Take 1/2  of the 'x' component......square it ....and add it to both sides

x^2 + 2x + '1' = -4 + 1    simplify

(x+1)^2 = -3       Solve

x+1 =  sqrt(-3)

x = -1 +- sqrt(-3)

ElectricPavlov  Sep 18, 2018
 #1
avatar+14592 
+2
Best Answer

Perform the same operation on BOTH sides of the equation .Always add the same amounts to BOTH sides of the equation. 

 

Divide by 5 to get leading coefficient of the x^2 term to equal '1'.....necessary for 'Completing theSquare' operation

 

5x^2  + 10x +20 = 0      DIvide both sides of the equation by '5'

x^2 + 2x + 4 = 0   re-arrange

x^2 + 2x = -4

 

Take 1/2  of the 'x' component......square it ....and add it to both sides

x^2 + 2x + '1' = -4 + 1    simplify

(x+1)^2 = -3       Solve

x+1 =  sqrt(-3)

x = -1 +- sqrt(-3)

ElectricPavlov  Sep 18, 2018

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