Radical equations

• 1). Isolate the radical. If the problem is the square root of (x) +2 = 4, subtract two from both sides of the equation: square root x = 4-2. If equations occur inside the radical symbol, the square root includes x+2, so keep them together: square root of (x+2) = 4. The square root is on one side of the equation.
  
  
• 2). Isolate the variable. In the case of radical equations, this usually involves squaring both sides of the equation. Square both sides as a whole, not the individual numbers. In the radical equation square root x = 4-2, it would be correct to square the sum of 4-2, (4-2)² not 4²-2².
  
  
• 3). Check the answer. In this equation, x=4. Put the answer in the place of the variable to check for accuracy: square root 4 = 4-2, which is simplified to 2 = 2.
  
  

Quadratic Equations

• 1). Put the problem in classic quadratic form. Move all variables to the left of the equation. Expand equations to remove any brackets.
  
  
• 2). Isolate the x using the quadratic formula: x = [-b +or- square root (b² - 4ac)]/2a. Note that you will be arriving at two answers, one on the negative spectrum and one on the positive.
  
  
• 3). Insert numbers for a, b and c coefficients. Let’s say a=1, b=5 and c=6. The equation would look like this: x = [-5 +or- square root (5²-4x1x6)]/2x1.
  
  
• 4). Solve the equation twice, using + for one and – for the other: x = [-5 + square root (25-24)] / 2 and x = [-5 - square root (25-24)] / 2.
  
  
• 5). Simplify the equations: x = (-5+1)/2, or x = -2. The other equation would break down to x = (-5–1)/2 or x = -3.
  
  
• 6). Check the work. Replace your value for x in the original equation to see if it works.