The product of two consecutive positive even numbers is 528. What are the numbers? (Enter solutions from smallest to largest.)
and
x(x+2)=528
x^2+2x=528.
At this point complete the square
(x+1)^2=529
x+1=+/-square root 529
x=-1+/-23
The two solutions are 22,-24. Remember that is wants even integers.
22(24)=528
Let's assume the two consecutive positive even numbers are x and x+2.
According to the given information, the product of these two numbers is 528. Hence, we can write the equation as follows:
x * (x+2) = 528
Now, let's solve this equation step-by-step:
Expand the equation:
x^2 + 2x = 528
Rearrange to have all terms on one side:
x^2 + 2x - 528 = 0
Now, we can factor this quadratic equation:
(x - 22)(x + 24) = 0
Setting each expression equal to zero, we have two possible solutions:
x - 22 = 0 or x + 24 = 0
Solving for x in each case:
x = 22 or x = -24
Since we are looking for positive even numbers, we can reject the negative solution of x = -24.
Therefore, the two consecutive positive even numbers that have a product of 528 are 22 and 24.
To find the two consecutive positive even numbers whose product is 528, we can set up an equation and solve for the unknown numbers.
Let's assume the first even number is x, then the next consecutive positive even number would be x + 2, since the numbers are consecutive even numbers.
According to the problem, the product of these two numbers is 528. So, we can set up the equation:
x * (x + 2) = 528
Expanding the equation, we get:
x^2 + 2x = 528
Rearranging the equation, we have a quadratic equation:
x^2 + 2x - 528 = 0
To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. In this case, let's use factoring.
Factoring the quadratic equation, we get:
(x - 22)(x + 24) = 0
Setting each factor equal to zero and solving for x, we have:
x - 22 = 0 or x + 24 = 0
Solving for x in each equation, we get two possible values:
x = 22 or x = -24
Since we are looking for positive even numbers, we can disregard the negative value. Therefore, the first even number is 22.
To find the next consecutive positive even number, we add 2 to the first even number:
22 + 2 = 24
So, the two consecutive positive even numbers whose product is 528 are 22 and 24.