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

#1**+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**+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