Question

a rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. the equation (x + 5)x = 104 represents the situation, where x represents the width of the rectangle. the first step in solving by factoring is to write the equation in standard form, setting one side equal to zero. what is the equation for the situation, written in standard form?\
\\( x^2 - 99 = 0 \\)\
\\( x^2 - 99x = 0 \\)\
\\( x^2 + 5x + 104 = 0 \\)\
\\( x^2 + 5x - 104 = 0 \\)

Explanation:

Step1: Expand the left - hand side of the equation

The given equation is \((x + 5)x=104\). Using the distributive property \(a(b + c)=ab+ac\), where \(a = x\), \(b=x\) and \(c = 5\), we get \(x\times x+x\times5=104\), which simplifies to \(x^{2}+5x = 104\).

Step2: Rewrite in standard form

The standard form of a quadratic equation is \(ax^{2}+bx + c = 0\) (\(a
eq0\)). To get this form from \(x^{2}+5x = 104\), we subtract 104 from both sides of the equation.
So, \(x^{2}+5x-104=104 - 104\), which simplifies to \(x^{2}+5x - 104=0\).

Answer:

D. \(x^{2}+5x - 104=0\)