Question

21x = 196 – x²

Answer 1

Given: 21x = 196 – x²

On rewriting the given equation in the standard form of the quadratic equation, we get:

x² + 21x – 196 = 0

On splitting the middle term 21x as 28x – 7x, we get:

x² + 28x – 7x – 196 = 0

$\Rightarrow$x(x + 28) – 7(x + 28) = 0

$\Rightarrow$(x + 28) (x – 7) = 0

We know that if the product of two numbers is zero, then at least one of them must be zero.

Thus,

x + 28 = 0 or x – 7 = 0

$\Rightarrow$x = –28 or x = 7

Therefore, the solution of the given equation is x = –28, 7.