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Comprehensive Guide to Solving Linear and Quadratic Equations

This guide covers essential methods for solving linear equations in one variable, including those with fractions. Additionally, it delves into rational equations, absolute value equations, and provides examples for each type. The tutorial further explores quadratic equations, focusing on factoring, the square root property, completing the square, and using the quadratic formula. It also discusses the discriminant and the significance of graphing in determining the solutions, known as zeros, that correspond to the x-intercepts of the quadratic function.

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Comprehensive Guide to Solving Linear and Quadratic Equations

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  1. Section P7Equations

  2. Solving Linear Equations in One Variable

  3. Example

  4. Linear Equations with Fractions

  5. Solving with Fractions

  6. Example

  7. Example

  8. Rational Equations

  9. Solving Rational Equations

  10. Example

  11. Example

  12. Example

  13. Solving a Formula for One of Its Variables

  14. Example

  15. Example

  16. Equations Involving Absolute Value

  17. Example

  18. Example

  19. Quadratic Equations and Factoring

  20. Example

  21. Example

  22. Example

  23. Quadratic Equations and the Square Root Property

  24. Example

  25. Example

  26. Quadratic Equations and Completing the Square

  27. Obtaining a Perfect Square Trinomial

  28. Completing the Square

  29. Example

  30. Example

  31. Example

  32. Quadratic Equations and the Quadratic Formula

  33. Example

  34. Example

  35. Quadratic Equations and the Discriminant

  36. Example

  37. Graphing Calculator The real solutions of a quadratic equation ax2+bx+c=0 correspond to the x-intercepts of the graph. The U shaped graph shown below has two x intercepts. When y=0, the value(s) of x will be the solution to the equation. Since y=0 these are called the zeros of the function.

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