The quadratic equationx2−8x=−20 is to be solved by completing the square. Which equation would be a step in that solution?A. (x−4)2=4B: x2−8x+16=−20+16C: x2−8x+20=0D. x2−8x+16=−20
Q. The quadratic equation x2−8x=−20 is to be solved by completing the square. Which equation would be a step in that solution?A. (x−4)2=4B: x2−8x+16=−20+16C: x2−8x+20=0D. x2−8x+16=−20
Understand Completing the Square: Understand the process of completing the square.To complete the square for a quadratic equation in the form x2+bx=c, we need to add (2b)2 to both sides of the equation to form a perfect square trinomial on the left side.
Identify Coefficient: Identify the coefficient b in the given equation.In the equation x2−8x=−20, the coefficient b is −8.
Calculate (b/2)2: Calculate (b/2)2. We need to calculate (−8/2)2 to find the value to add to both sides of the equation. (−8/2)2=(−4)2=16
Add to Both Sides: Add (2b)2 to both sides of the equation.We add 16 to both sides of the equation x2−8x=−20 to complete the square.x2−8x+16=−20+16
Check Answer Choices: Check the answer choices to see which one matches the step we just performed.The correct step in completing the square is represented by the equation where we have added 16 to both sides.
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