Solve the following quadratic equations using the quadratic formula. x^2+6x=0?

Answer 1

The quadratic formula states the the solutions to the equation ax^2 + bx + c = 0, where a is nonzero, are
x = [-b +/- sqrt(b^2 -4ac)] / (2a)

a is the coefficient of x^2, b is the coefficient of x, and c is the constant.

x^2 + 6x = 0
a = 1, b = 6, and c = 0

Plugging in to the quadratic formula,
x = [-6 +/- sqrt((6)^2 -4(1)(0))] / (2*1)
x = [-6 +/- sqrt(36-0)] / 2
x = [-6 +/- sqrt(36)] / 2
x = [-6 +/- 6] / 2

x = [-6+6] / 2 or x = [-6-6] / 2
x = 0/2 or x = -12/2
x = 0 or x = -6

Factoring would be a lot quicker, but sometimes your instructor wants to make sure you know how to use the quadratic formula.

Answer 2

Quadratic formula is a little overkill for this one. Either x=0 or x = -6 by factoring:

x(x + 6) = 0