Two roots, one usable answer: solve a rectangle problem
A quadratic equation describes a model. Its roots must still satisfy the original dimensions, units and physical restrictions.
Quadratic equation →Build the equation from dimensions
A rectangular panel has area 24 square metres and a length 2 metres greater than its width. Let the width be x metres, so the length is x+2. Then x(x+2)=24, or x²+2x−24=0. Enter a=1, b=2 and c=−24. Writing the variables and units before calculating makes it clear what each resulting root would represent.
Filter the mathematical solutions
The roots are 4 and −6. Both satisfy the algebraic equation, but a physical width must be positive. Choose width 4 metres and length 6 metres; their product is 24 square metres. The negative root is not a calculator error. It is a valid algebraic solution excluded by the physical domain of the model you created.
Verify assumptions before ordering materials
Use the rectangle-area tool to check the chosen dimensions and perimeter. This model assumes a true rectangle and exact area and difference measurements; it does not include tolerances, trimming, joints or waste. If the given area is approximate, the dimensions are estimates too. Other applications may accept both roots, one root or neither, so never discard all negative roots automatically without considering what the variable means. The width restriction x>0 was known before solving and should be recorded as part of the model.
Try the calculators
- Quadratic equation
Solve for real or complex roots.
- Scientific calculator
Arithmetic, powers, trigonometry and logarithms.
- Rectangle area
Calculate a rectangle’s area and perimeter.