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The quadratic equation x28x=20x^{2}-8x=-20 is to be solved by completing the square. Which equation would be a step in that solution?\newlineA. (x4)2=4(x-4)^{2}=4\newlineB: x28x+16=20+16x^{2}-8x+16=-20+16\newlineC: x28x+20=0x^{2}-8x+20=0\newlineD. x28x+16=20x^2-8x+16=-20

Full solution

Q. The quadratic equation x28x=20x^{2}-8x=-20 is to be solved by completing the square. Which equation would be a step in that solution?\newlineA. (x4)2=4(x-4)^{2}=4\newlineB: x28x+16=20+16x^{2}-8x+16=-20+16\newlineC: x28x+20=0x^{2}-8x+20=0\newlineD. x28x+16=20x^2-8x+16=-20
  1. Understand Completing the Square: Understand the process of completing the square.\newlineTo complete the square for a quadratic equation in the form x2+bx=cx^2 + bx = c, we need to add (b2)2(\frac{b}{2})^2 to both sides of the equation to form a perfect square trinomial on the left side.
  2. Identify Coefficient: Identify the coefficient bb in the given equation.\newlineIn the equation x28x=20x^2 - 8x = -20, the coefficient bb is 8-8.
  3. Calculate (b/2)2(b/2)^2: Calculate (b/2)2(b/2)^2. We need to calculate (8/2)2(-8/2)^2 to find the value to add to both sides of the equation. (8/2)2=(4)2=16(-8/2)^2 = (-4)^2 = 16
  4. Add to Both Sides: Add (b2)2(\frac{b}{2})^2 to both sides of the equation.\newlineWe add 1616 to both sides of the equation x28x=20x^2 - 8x = -20 to complete the square.\newlinex28x+16=20+16x^2 - 8x + 16 = -20 + 16
  5. Check Answer Choices: Check the answer choices to see which one matches the step we just performed.\newlineThe correct step in completing the square is represented by the equation where we have added 1616 to both sides.

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