If x(x - 9) = -20, which of the following is a possible value of x? — SAT

If $x(x - 9) = -20$ , which of the following is a possible value of $x$ ?

To solve the equation

x(x - 9) = -20

, first distribute the

x

to get

x^2 - 9x = -20

. Next, rewrite the equation in standard form by adding

20

to both sides, which gives

x^2 - 9x + 20 = 0

. Factoring the quadratic expression yields

(x - 4)(x - 5) = 0

. Applying the zero product property gives two possible solutions:

x = 4

and

x = 5

. Therefore, the value

5

is a possible value of

x

Distribute

x

on the left side of the equation.

x^2 - 9x = -20

Expanding the product allows the quadratic equation to be rewritten in standard form.

Add

20

to both sides to set the equation to standard form

ax^2 + bx + c = 0

x^2 - 9x + 20 = 0

Setting the quadratic equation to equal zero is necessary to solve by factoring or using the quadratic formula.

Factor the quadratic trinomial by finding two integers that multiply to

20

and add to

-9

(x - 4)(x - 5) = 0

The numbers

-4

and

-5

satisfy these conditions, allowing the expression to be factored.

Set each factor equal to zero to find the possible values of

x

x = 4

x = 5

According to the zero product property, if the product of two factors is zero, then at least one of the factors must be zero.

Solving quadratic equations by factoring

Question