A: Solve the following equation:
k2 + 4k = 0
A: By factoring
B: By using the quadratic formula
A. Have you tried to factor it?
B. The quadratic formula, for an expression ax^2 + bx + c, states that x = (-b +/- sqrt(b^2 - 4ac) ) / (2a). Use the given values of a, b, and c to find the solutions for x.
To solve the equation k^2 + 4k = 0, you have two common methods: factoring and using the quadratic formula. I will explain both methods, and you can choose the one you prefer.
Method A: Factoring
To solve the equation by factoring, you want to express the equation as a product of two binomials. In this case, k^2 + 4k = 0 can be factored as k(k + 4) = 0. Since the product of two numbers equals zero if and only if at least one of the numbers is zero, we can set each factor equal to zero and solve for k.
k = 0 (Equation 1)
k + 4 = 0 (Equation 2)
From Equation 1, we find that k = 0. From Equation 2, we subtract 4 from both sides to get k = -4. So, the two solutions to the equation are k = 0 and k = -4.
Method B: Quadratic Formula
If you prefer to use the quadratic formula to solve the equation, the formula states that for an equation in the form ax^2 + bx + c = 0, the solutions are given by the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For your equation k^2 + 4k = 0, we can see that a = 1, b = 4, and c = 0. Plugging these values into the quadratic formula, we get:
k = (-4 ± √(4^2 - 4(1)(0))) / (2(1))
k = (-4 ± √(16)) / 2
k = (-4 ± 4) / 2
This simplifies to:
k = (-4 + 4) / 2 = 0 / 2 = 0 or k = (-4 - 4) / 2 = -8 / 2 = -4
So again, the two solutions to the equation are k = 0 and k = -4.