silemus.
← All examples
  1. 1Solving 7(x−2)=3x+10
  2. 2Solving a rational equation
  3. 3Solving 5−3x≤17
  4. 5Slope between two points
  5. 6Line through two points
  6. 7Slope and intercept from 3x−4y=12
  7. 8Parallel line through a point
  8. 10Solving a system by substitution
  9. 11Elimination, 2 equations
  10. 14Exponent rules, same base
  11. 15Fractional exponent, 27^(2/3)
  12. 17Simplifying root sums
  13. 20Solving 3^(x+1)=81
  14. 21Factoring x²−5x−24
  15. 23Difference of squares
  16. 24Quadratic formula
  17. 26Vertex of a parabola
  18. 27Discriminant of a quadratic
  19. 28One solution, discriminant=0
  20. 30Expanding a binomial times trinomial
  21. 31Evaluating f(-2)
  22. 34Exponential growth, 5% a year
  23. 35Half-life decay
  24. 37Solving |2x−5|=9
  25. 39Simplifying a rational expression

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.

How good is this answer?