There are TWO solutions to a quadratic equation. Unless otherwise instructed, give both answers if it is a pure math problem. For real worldproblems and story problems, one of the answers is usually ridiculous and can be ignored. Do a sanity check to identify the applicable solution. In the case of a story problem, if you are unsure which solution is correct, give both. For each of the following, set up either a system of equations in two variables or a quadratic equation and solve. (Round to two decimal places if necessary.)The area of a square is 196 sq in. Find its side length.Carpentry The perimeter of a rectangular door is 22 ft. Its length is 2 ft more than twice its width. Find the dimensions of the door.Sheet Metal Trades The length of a rectangular piece of sheet steel is 2 in. longer than the width. Find the exact dimensions if the area of the sheet is 168 sq inLandscaping The perimeter of a rectangular field is 750 ft. If the length is four times the width, find the dimensions of the field.2.4.8.10.12.16.18.20.Painting A painter mixes paint worth $28 per gallon with paint worth $34 per gallon. He wishes to make 15 gal of a mixture worth $32 per gallon. How many gallons of each kind of paintmust be included in the mixture?Aviation The lift L (in pounds) on a certain type of airplane wing is given by the formulaL = 0.083v²where v is the speed of the airflow over the wing (in feet per second). What air speed is required to provide a lift of 2500 lb? (Round to the nearest ten feet per second.)Electronics For a certain temperature-sensitive electronic device, the voltage output V (in millivolts) is given by the formulaV = 3.1T-0.0147²where T is the temperature (in degrees Celsius). What temperature is needed to produce a voltage of 150 mV?Automotive Trades The fuel economy Fof a certain hybrid electric car at speeds between 50 mi/hr and 100 mi/hr is given by the formulaF = 0.005v21.25v +96where Fis in miles per gallon and vis the speed in miles per hour. What speed will result in a fuel economy of 39 mi/gal?

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For each of the following, set up either a system of equations in two variables or a quadratic equation and solve. (Round to two decimal places if necessary.) 2. The area of a square is 196 sq in. Find its side length.