Question

Solve the equation by completing the square. x2 + 20x + 82 = 7

Answer 1

Answer:

  {-15, -5}

Step-by-step explanation:

The constant on the left needs to be the square of half the x-coefficient:

  (20/2)^2 = 100

To get it to that value, we can add 18 to both sides of the equation:

  x^2 +20x +100 = 25 . . . add 18 to both sides of the equation

  (x +10)^2 = 25 . . . . . . .  . write the left side as a square

  x +10 = ±√25 = ±5 . . . . . take the square root

  x = -10 ±5 = {-15, -5}

The solutions are x = -15 and x = -5.

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The attached graph shows the solutions to ...

  x^2 +20x +82 -7 = 0 . . . . . the result of subtracting 7 from both sides