Question

quadratic word problems 56 49% 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 need to factor \(x^2 + 4x - 32 = 0\). We look for 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

Set each factor equal to zero:

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

Answer:

The lower number is \(4\).