Find the solutions :What type of equation is (3+x)(1+x)=24 ?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The equation (3+x)(1+x)=24 can be written as

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

open the brackets

3 + x + 3x + x^2 = 24

=> x^2 + 4x + 3 = 24

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

This is a quadratic equation as the highest power of x is 2.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll simplify and we'll get:

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

We'll remove the brackets:

3 + 3x +  x + x^2  - 24 = 0

We'll combine like terms:

x^2 + 4x - 21 = 0

Since the maximum order of the equation is 2, the equation is a quadratic.

The number of the roots is 2 and the formula for finding the roots is:

x1 = [-b+sqrt(b^2 - 4ac)]/2a

x2 = [-b-sqrt(b^2 - 4ac)]/2a

We'll identify a,b,c:

a = 1

b = 4

c = -21

x1 = [-4+sqrt(16+84)]/2

x1 = (-4+10)/2

x1 = 3

x2 =  (-4-10)/2

x2 = -7

The solutions of the quadratic equation are {-7 ; 3}.

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