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Solve x^2 - 6x + 13 = 0

Worked through step by step. More quadratics.

Answer
x=3+2i,x=3−2i\boxed{x = 3 + 2i, \quad x = 3 - 2i}

Substituting either complex root back into the original equation yields zero, confirming the solution is correct.

Problem: Solve the quadratic equation x2−6x+13=0x^2 - 6x + 13 = 0.

Steps

  1. Complete the square
    (x−3)2+4=0(x - 3)^2 + 4 = 0
  2. Subtract 4 from both sides
    (x−3)2=−4(x - 3)^2 = -4
  3. Apply the square root property
    x−3=±−4x - 3 = \pm \sqrt{-4}
  4. Simplify the radical using imaginary units
    x−3=±2ix - 3 = \pm 2i
  5. Add 3 to both sides
    x=3±2ix = 3 \pm 2i

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