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There are many methods to do this but there are few shorter than this one.

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Steps

  1. Convert a Quadratic Formula to Roots Form by Completing the Square Step 1.jpg
    1
    Write down each formula step please. Let's start with ax^2 +bx +c = y = 0. We are setting the y value to 0 to find the intercepts on the x axis. where y=0.
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  2. Convert a Quadratic Formula to Roots Form by Completing the Square Step 2.jpg
    2
    Subtract c from both sides and obtain ax^2 + bx = -c
  3. Convert a Quadratic Formula to Roots Form by Completing the Square Step 3.jpg
    3
    Multiply both sides by 4a to obtain 4a^2x^2 + 4abx = -4ac
  4. Convert a Quadratic Formula to Roots Form by Completing the Square Step 4.jpg
    4
    Complete the square on the left and add b^2 to the right side: (2ax + b)^2 = b^2 - 4ac. You may want to multiply (2ax + b)^2 out to make sure everything is OK. It's a good practice to follow.
  5. Convert a Quadratic Formula to Roots Form by Completing the Square Step 5.jpg
    5
    Take the square root of both sides to obtain (2ax + b) = ± sqrt(b^2 - 4ac)
  6. Convert a Quadratic Formula to Roots Form by Completing the Square Step 6.jpg
    6
    Subtract b from both sides, then divide both by 2a to obtain x = (-b ± sqrt(4ac))/2a.
  7. Convert a Quadratic Formula to Roots Form by Completing the Square Step 7.jpg
    7
    Since there are two x roots, depending on the ±, restate as {x1, x2} = (-b ± sqrt(4ac))/2a.
  8. 8
    If you find a shorter version, please let me know.
  9. 9
    It's good practice to also work it backwards to the original form, i.e. derive the Quadratic Formula. Try that now if you please.
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Categories: Algebra

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