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?
+36916 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)
+36916 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)
