Michelle decides she is going to cover only half of her living room with the new flooring, and
paint the other half, meaning she will cover only 24√6
square feet with the new flooring
1. After carefully measuring the exposed concrete, she determines 6 square feet are already
painted and the remaining unpainted area forms a square with
side length x. The entire
area of concrete,
including the painted and unpainted portions
, is a total of 55 square feet.
Michelle
determines the equation x+6-55 would help
determine the side length x of
the square she
needs to paint. Is Michelle's equation correct?
Explain your reasoning.
2. Solve Michelle's equation by completing the square and the square root method. What is
the side length x of the square to be painted? Be sure to include
units in your answer.
3. Juan comes over to help Michelle with his handy room-scanner. The room-scanner
device is designed to scan an area and give the user
the exact dimensions. When Juan
scans the area Michelle is not covering with new
flooring, the room-scanner gives him an
ERROR message and reads out AREA-2x+15x+1. Juan
isn't sure how that helps
Michelle and he needs your help determining
if this equation can be solved for an x value
close to what Michelle got by solving her
equation. Solve Juan's equation from the room-
scanner using the quadratic formula. Be sure to leave
your answer as a simplified radical
expression and include units.
4. Convert Juan's value of x for the side length of the square to a decimal and compare it to
the value you determined in #2. Is Juan's room-
scanner close to the value of x Michelle's
equation produces?
5. When Michelle goes to buy her flooring, the flooring specialist only sells flooring in bulk
quantities measuring √55
feet long by √√66 feet wide. Write these dimensions as rational
exponents and then
determine if the area of the bulk quantity will cover a square with
side length 8 feet.