Solving Quadratic Equations By Extracting Square Root

• Perfect squares


  Numbers like 1, 4, 9, 16, 25, 36 and so on
• Quadratic equations


  Equations that can be solved by extracting square roots
• Solving quadratic equations by extracting square roots

  1. Get the square root of both sides

  2. If the result is a perfect square, the solution is the positive or negative square root

  3. If the result is not a perfect square, find the factors that make it a perfect square, then extract the square root
• 49 is a perfect square
• 169 is a perfect square
• 75 is not a perfect square
• Solving x^2 = 75


  1. Get the square root of both sides

  2. Find factors of 75 that make a perfect square (25 x 3)

  3. The solution is x = ±√(25 x √3)
• Solving x^2 = 80


  1. Get the square root of both sides

  2. Find factors of 80 that make a perfect square (16 x 5)

  3. The solution is x = ±√(16 x √5)
• Solving 2(x-5)^2 = 32


  1. Divide both sides by 2

  2. Get the square root of both sides

  3. The solutions are x = 9 and x = 1
• Solving 3(4x-1)^2 - 1 = 11

  1. Rearrange to 3(4x-1)^2 = 12

  2. Divide both sides by 3

  3. Get the square root of both sides

  4. The solutions are x = 3/4 and x = -1/4
• Solving (2x-3)^2 = 18


  1. Get the square root of both sides

  2. Find factors of 18 that make a perfect square (9 x 2)

  3. The solutions are x = (3√2 + 3)/2 and x = (3-3√2)/2
• Solving 2(5x+2)^2 = 64


  1. Divide both sides by 2

  2. Get the square root of both sides

  3. Find factors of 32 that make a perfect square (16 x 2)

  4. The solutions are x = (-2 + 4√2)/5 and x = (-2 - 4√2)/5
• Quadratic Equation


  An equation of the form ax² + bx + c = 0, where a, b, and c are constants.
• Square Root


  A value that, when multiplied by itself, gives the original number.
• Isolate


  To rearrange an equation so that one variable is on one side and all other terms are on the other side.
• Verification


  The process of checking if the solutions satisfy the original equation.
• ± Symbol

  Indicates that there are two possible values: one positive and one negative.
• Perfect Square


  A number that is the square of an integer (e.g., 1, 4, 9, 16).
• Standard Form


  The standard representation of a quadratic equation: ax² + bx + c = 0.