1. Section P7 Equations

2. Solving Linear Equations in One Variable

6. Example

7. Linear Equations with Fractions

8. Solving with Fractions

9. Example

10. Example

11. Rational Equations

13. Solving Rational Equations

14. Example

15. Example

16. Example

17. Solving a Formula for One of Its Variables

19. Example

20. Example

21. Equations Involving Absolute Value

23. Example

24. Example

26. Quadratic Equations and Factoring

28. Example

29. Example

30. Example

31. Quadratic Equations and the Square Root Property

33. Example

34. Example

35. Quadratic Equations and Completing the Square

37. Obtaining a Perfect Square Trinomial
Start
Add
Result
Factored Form

38. Completing the Square

39. Example

40. Example

41. Example

42. Quadratic Equations and the Quadratic Formula

45. Example

46. Example

47. Quadratic Equations and the Discriminant

49. Example

50. 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.

51. Solving Polynomial Equations using the Graphing Calculator
By pressing 2nd Trace to get Calc, then the #2,you get the zeros. It will ask you for left and right bounds, and then a guess. For left and right bounds move the blinking cursor (using the arrow keys-cursor keys) to the left and press enter. Then move the cursor to the right of the x intercept and press enter. Press enter when asked to guess. Then you get the zeros or solution.
Repeat this process for each x intercept.

53. Determining Which Method to Use

55. Example

56. Example

57. Example

58. Radical Equations

59. A radical equation is an equation in which the variable occurs in a square root, cube root, or any higher root. We solve the equation by squaring both sides.

60. This new equation has two solutions, -4 and 4
This new equation has two solutions, -4 and 4. By contrast, only 4 is a solution of the original equation, x=4. For this reason, when raising both sides of an equation to an even power, check proposed solutions in the original equation.
Extra solutions may be introduced when you raise both sides of a radical equation to an even power. Such solutions, which are not solutions of the given equation are called extraneous solutions or extraneous roots.

63. Example
Solve and check your answers:

64. (a)
(b)
(c)
(d)

65. (a)
(b)
(c)
(d)