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dratic equation x^(2)+12 x+8=0 by completing the square.

dratic equation x2+12x+8=0 x^{2}+12 x+8=0 by completing the square.

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Full solution

Q. dratic equation x2+12x+8=0 x^{2}+12 x+8=0 by completing the square.
  1. Move Constant Term: First, let's move the constant term to the other side of the equation: x2+12x=−8x^2 + 12x = -8
  2. Complete the Square: Now, to complete the square, we need to add (b2)2(\frac{b}{2})^2 to both sides. Here, bb is the coefficient of xx, which is 1212.(122)2=62=36\left(\frac{12}{2}\right)^2 = 6^2 = 36So we add 3636 to both sides:x2+12x+36=−8+36x^2 + 12x + 36 = -8 + 36
  3. Simplify Right Side: Simplify the right side of the equation: x2+12x+36=28x^2 + 12x + 36 = 28
  4. Perfect Square: Now we have a perfect square on the left side: (x+6)2=28(x + 6)^2 = 28

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