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Place the steps in the correct order to solve the following equation using the quadratic formula.

x2 − 10x = 12


(6 points)
Arrange responses in the correct order to answer the question. Select a response, navigate to the desired position and insert response at that position. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can be moved using the up and down arrow keys or by dragging with a mouse.

1 answer

To solve the equation \( x^2 - 10x = 12 \) using the quadratic formula, the steps should be arranged as follows:

  1. Rearrange the equation to standard form: Move all terms to one side to form \( ax^2 + bx + c = 0 \).

    • This gives us \( x^2 - 10x - 12 = 0 \).

  2. Identify coefficients a, b, and c: From the standard form \( ax^2 + bx + c = 0 \), identify

    • \( a = 1 \),
    • \( b = -10 \),
    • \( c = -12 \).

  3. Use the quadratic formula: The quadratic formula is given by \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).

  4. Calculate the discriminant: Find \( b^2 - 4ac \).

    • Calculate \( (-10)^2 - 4(1)(-12) = 100 + 48 = 148 \).

  5. Substitute values into the quadratic formula:

    • Now plug in the values into the quadratic formula:
    • \( x = \frac{-(-10) \pm \sqrt{148}}{2(1)} \).

  6. Simplify to find the values of x:

    • This results in \( x = \frac{10 \pm \sqrt{148}}{2} \).
    • You can further simplify \( \sqrt{148} = 2\sqrt{37} \), giving \( x = \frac{10 \pm 2\sqrt{37}}{2} = 5 \pm \sqrt{37} \).

So the steps in order are:

  1. Rearrange the equation to standard form.
  2. Identify coefficients a, b, and c.
  3. Use the quadratic formula.
  4. Calculate the discriminant.
  5. Substitute values into the quadratic formula.
  6. Simplify to find the values of x.