Solve the following equation:
k2 + 4k = 0
By factoring and By using the quadratic formula
Can someone please help me to understand how to this problem...I do not understand the steps to get the correct answer.
Thanks!!!
2k + 4k = 0
First, combine like terms. In this case, the k's:
6k = 0
Simplify by dividing by 6 on both sides:
6k/6 = k
0/6 = 0
So,
k = 0
Of course, I'd be happy to help you understand how to solve this equation!
To solve the equation k^2 + 4k = 0, we can either factor or use the quadratic formula.
1. Factoring:
Factoring involves finding two numbers that multiply to the constant term (in this case, 0), and add up to the coefficient of the linear term (in this case, 4). Since 0 multiplied by any number is still 0, one of the factors must be 0. So we have k(k + 4) = 0.
Now we set each factor equal to zero and solve for k:
k = 0, and k + 4 = 0
For k + 4 = 0, we subtract 4 from both sides, which gives us:
k = -4
So the two solutions are k = 0 and k = -4.
2. Quadratic Formula:
The quadratic formula is a general method to find the solutions to any quadratic equation of the form ax^2 + bx + c = 0. In this case, a = 1, b = 4, and c = 0.
The quadratic formula is:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
Plugging in the values, we have:
k = (-4 ± sqrt(4^2 - 4(1)(0))) / (2(1))
This simplifies to:
k = (-4 ± sqrt(16)) / 2
k = (-4 ± 4) / 2
Now we have two possibilities:
1. k = (-4 + 4) / 2 = 0 / 2 = 0
2. k = (-4 - 4) / 2 = -8 / 2 = -4
So again, we find that the solutions are k = 0 and k = -4.
Both methods give the same solutions. You can choose which method you are more comfortable with or the method that seems simpler for a particular equation.