If x > 0 and x^2 - 3x - 18 = 0, what is the value of x + 2? — SAT

If $x > 0$ and $x^2 - 3x - 18 = 0$ , what is the value of $x + 2$ ?

Factoring the quadratic equation

x^2 - 3x - 18 = 0

yields

(x - 6)(x + 3) = 0

. This gives two solutions:

x = 6

and

x = -3

. Since the condition specifies

x > 0

, we choose

x = 6

. The question asks for the value of

x + 2

, which is

6 + 2 = 8

Factor the quadratic equation

x^2 - 3x - 18 = 0

by finding two numbers that multiply to

-18

and add to

-3

(x - 6)(x + 3) = 0

Factoring allows us to find the individual roots of the quadratic equation.

Solve for the possible values of

x

by setting each factor equal to zero.

x = 6

x = -3

If the product of two factors is zero, then at least one of the factors must equal zero.

Apply the given constraint that

x > 0

x = 6

The problem specifies that

x

must be a positive number, so the negative root

x = -3

must be discarded.

Substitute the value of

x

into the expression

x + 2

The question asks for the value of

x + 2

, so we evaluate

6 + 2

Solving quadratic equations by factoring and applying constraints on roots

Estimated Time:1m 0s

Question