Question

the product of a positive number and four more than the number is 32. use x for the lower number. what is the lower number? equation $x^{2}+4x - 32 = 0$ solution?

Explanation:

Step1: Factor the quadratic equation

We have the equation \(x^{2}+4x - 32=0\). We need to find two numbers that multiply to \(- 32\) and add up to \(4\). The numbers are \(8\) and \(-4\) since \(8\times(-4)=-32\) and \(8+( - 4)=4\). So we can factor the equation as \((x + 8)(x-4)=0\)

Step2: Solve for x

Using the zero - product property, if \((x + 8)(x - 4)=0\), then either \(x+8 = 0\) or \(x - 4=0\).

• For \(x+8=0\), we get \(x=-8\). But the problem states that \(x\) is a positive number, so we discard this solution.
• For \(x - 4=0\), we get \(x = 4\)

Answer:

The lower number is \(4\)