Question

the product of two consecutive positive numbers is 30. use x for the lower number. what is the lower number? equation $x^2 + x - 30 = 0$ solution?

Explanation:

Step1: Factor the quadratic equation

We need to factor \(x^{2}+x - 30=0\). We look for two numbers that multiply to \(- 30\) and add up to \(1\). The numbers are \(6\) and \(-5\) since \(6\times(-5)=-30\) and \(6+( - 5)=1\). So we can write the equation as \((x + 6)(x-5)=0\)

Step2: Solve for x

Set each factor equal to zero:

• For \(x + 6=0\), we get \(x=-6\)
• For \(x - 5=0\), we get \(x = 5\)

Since we are looking for positive numbers, we discard \(x=-6\).

Answer:

The lower number is \(5\)