Solving Quadratic equations by extracting the square roots

• What is the general form of a quadratic equation?


  x² = K
• What happens if \( K > 0 \) in a quadratic equation?

  It has two real solutions.
• What is the formula for the roots of a quadratic equation when \( K > 0 \)?

  x = \pm \sqrt{K}
• What occurs if \( K = 0 \) in a quadratic equation?

  It has one real solution, \( x = 0 \).
• What is the outcome if \( K < 0 \) in a quadratic equation?

  It has no solutions or roots.
• What are the steps to solve a quadratic equation by extracting the square roots?

  1. Write the equation in the form \( x² = k \).
  2. Use the square root property.
  3. Solve for \( x \).
  4. Simplify if possible.
• How do you solve the equation \( x² - 100 = 0 \)?

  First, rewrite it as \( x² = 100 \), then take the square root to find \( x = 10 \) and \( x = -10 \).
• What is the solution for the equation \( 2x² + 4 = 2 \)?

  Rewrite it as \( 2x² = 2 - 4 \), leading to \( x² = -1 \), which has no solution.
• What does the equation \( (x - 3) = 9 \) imply when solved?

  It implies \( x = 12 \) or \( x = -6 \) after simplifying.
• How do you solve the equation \( x² - 70 = 5 \)?

  Rewrite it as \( x² = 75 \) and then take the square root to find \( x = \sqrt{75} \).
• What is the square root of \( 25 \)?

  5
• What is the result of \( x² = 75 \) when simplified?

  x = \sqrt{75} \text{ or } x = -\sqrt{75}
• What is the simplified form of \( \sqrt{25} \)?

  5
• What does \( x = \frac{5}{3} \) represent in the context of quadratic equations?

  It represents one of the solutions to a quadratic equation.
• What are the properties of quadratic equations based on the value of \( K \)?

  • If \( K > 0 \): Two real solutions.
  • If \( K = 0 \): One real solution.
  • If \( K < 0 \): No solutions.