The value of k = - 14 and the other solution apart from x = 0 is x = -4.
Solving Quadratic equations
To solve the quadratic equation x² + 4x - 14 = k where one of the solutions is x = 0. This means that for us to be able to find the value of k, we need to replace the values of x in the quadratic equation with 0.
By doing so, we have:
0² + 4(0) - 14 = k
- 14 = k
Thus, the value of k is -14
We can now rewrite the equation x² + 4x - 14 = k as:
x² + 4x - 14 = -14
Add 14 to both sides
x² + 4x - 14 + 14 = - 14 + 14
x² + 4x = 0
Let's factor out x from x² + 4x = 0
x(x + 4) = 0
Let's set each factor to zero.
x = 0 or x + 4 = 0
x = 0 or x = -4
Thus, the value of k = - 14 and the other solution apart from x = 0 is x = -4.