Question

How do you solve:18(18)=x(x+15)

Answer 1

Hello!

$18(18)=x(x+15)$

The parentheses indicate multiplication; the 18(18) on the left side of the equation is 18 * 18. On the right side of the equation, you have x(x + 15); to simplify this, you would distribute the x--that means multiply each term inside the parentheses by x. This is the Distributive Property: $a(b + c) = ab + ac$. Let's do that.

$18(18)=x(x+15)$
$324= x^{2} +15x$

Now, you can subtract 324 from each side to set the equation equal to 0.

$324= x^{2} +15x$
$324-324= x^{2} +15x-324$
$0= x^{2} +15x-324$

This is a quadratic equation; to solve it, we may factor (if the equation is able to be factored) or we can use the Quadratic Formula. Let's see if we can factor. To factor, find two numbers whose sum is 15 and whose product is -324. Since 324 is negative, we know one of the numbers is negative and one of the numbers is positive (a negative times a positive is always negative), and that means one of the numbers is greater than 15...

27 - 12 = 15
27 * -12 = -324

The factored polynomial is: (x + 27)(x - 12).

To find its solutions, set the factors equal to 0 and solve for x.

x + 27 = 0
x = -27

x - 12 = 0
x = 12

Answer:
The solution of $18(18)=x(x+15)$ is -27 and 12.