Question

What are the solutions of the equation?

x^2+4x=21

a. 23, -27
b. 3, -7
c. -3, 7
d. 4.8, -4.8

Answer 1

Option (b) is correct.

The solution of the quadratic equation
`x^2+4x=21` is -7 and 3

Explanation:

Consider the given quadratic equation
`x^2+4x=21`

This can be rewritten as,
`x^2+4x-21=0`

We can solve the quadratic equation using middle term splitting method,

4x can be written as 7x-3x , we get,

`\Rightarrow x^2+4x-21=0`

`\Rightarrow x^2+7x-3x-21=0`

Taking terms common, we get,

`\Rightarrow  x(x+7)-3(x+7)=0`

Thus,
`\Rightarrow (x-3)(x+7)=0`

Thus, we get (x-3)= 0 or (x+7)= 0

this gives x = 3 or x = -7

Thus, the solution of the quadratic equation
`x^2+4x=21` is -7 and 3