silemus.
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  1. 1Solving 7(x−2)=3x+10
  2. 2Solving a rational equation
  3. 3Solving 5−3x≤17
  4. 4Compound inequality
  5. 5Slope between two points
  6. 6Line through two points
  7. 7Slope and intercept from 3x−4y=12
  8. 8Parallel line through a point
  9. 9Perpendicular line equation
  10. 10Solving a system by substitution
  11. 11Elimination, 2 equations
  12. 12Two-variable ticket problem
  13. 13Equal cost of two plans
  14. 14Exponent rules, same base
  15. 15Fractional exponent, 27^(2/3)
  16. 16Evaluating 16^(−3/4)
  17. 17Simplifying root sums
  18. 18Rationalising 6/root3
  19. 19Solving a square root equation
  20. 20Solving 3^(x+1)=81
  21. 21Factoring x²−5x−24
  22. 22Factoring 2x²+7x−15
  23. 23Difference of squares
  24. 24Quadratic formula
  25. 25Completing the square
  26. 26Vertex of a parabola
  27. 27Discriminant of a quadratic
  28. 28One solution, discriminant=0
  29. 29Max height, projectile motion
  30. 30Expanding a binomial times trinomial
  31. 31Evaluating f(-2)
  32. 32Composing f(g(2)), g(f(2))
  33. 33Inverse function value
  34. 34Exponential growth, 5% a year
  35. 35Half-life decay
  36. 36Compound interest formula
  37. 37Solving |2x−5|=9
  38. 38Absolute value inequality
  39. 39Simplifying a rational expression
  40. 40Solving rational equation

24Quadratic formula

Use the quadratic formula to solve x2−4x−1=0\displaystyle x^2 - 4x - 1 = 0. Give the answers to 3 decimal places.

The two roots are x ≈ 4.236 and x ≈ -0.236. Using a=1, b=-4, c=-1 in x = (-b ± √(b²-4ac))/2a gives (4 ± √20)/2, and √20 ≈ 4.472 splits into those two values. Check: 4.236² - 4(4.236) - 1 ≈ 0.

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