If x^2 - 9x + 18 = 0 and x > 4, what is the value of x? — SAT

If $x^2 - 9x + 18 = 0$ and $x > 4$ , what is the value of $x$ ?

Answer: 6

The value of

x

is 6.

Factoring the equation

x^2 - 9x + 18 = 0

gives

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

, which yields the solutions

x = 3

and

x = 6

. Applying the constraint

x > 4

, the only valid solution is 6.

Factor the quadratic equation

x^2 - 9x + 18 = 0

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

Finding two numbers that multiply to 18 and add to -9 allows us to write the quadratic expression in its factored form.

Solve for the roots of the equation.

x = 3

x = 6

By the zero product property, setting each factor to zero yields the possible solutions for the equation.

Apply the given constraint

x > 4

x = 6

Since the question specifies that

x

must be greater than 4, the root

x = 3

is discarded, leaving

x = 6

as the only valid solution.

Solving quadratic equations by factoring and applying constraints.

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