Is the equation 3 + x = 24 / ( x + 1 ) a quadratic?

### 2 Answers | Add Yours

You need to perform cross multiplication, such that:

`(3 + x)(x + 1) = 24 => 3(x + 1) + x(x + 1) = 24`

`3x + 3 + x^2 + x = 24 => x^2 + 4x + 3 - 24 = 0`

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

You may evaluate the solutions to quadratic equation, using quadratic formula, such that:

`x_(1,2) = (-4+-sqrt(16 + 84))/2 => x_(1,2) = (-4+-sqrt100)/2`

`x_(1,2) = (-4+-10)/2 => x_1 = 3 ; x_2 = -7`

**Hence, evaluating the solutions to the given quadratic equation, yields **`x_1 = 3 ; x_2 = -7.`

We'll have to multiply both sides by x+1:

3(x+1) + x(x+1) = 24

We'll remove the brackets:

3x + 3 + x^2 + x - 24 = 0

We'll combine like terms:

x^2 + 4x - 21 = 0

Since the order of the equation is two, therefore, the equation is a quadratic.

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes