$$ -x^{2}+6 x-3=0 $$ INSTRUCTION: Round your answers to two decimal places. Answer: $$ x=\square $$ or $$ x=\square $$

Question

UpStudy AI · Accepted Answer

We start with the equation:
  –x² + 6x – 3 = 0

Multiply every term by –1 to make it easier to solve:
  x² – 6x + 3 = 0

Now, using the quadratic formula where a = 1, b = –6, and c = 3:
  x = [–b ± √(b² – 4ac)] / (2a)

Substitute the given values:
  x = [6 ± √((–6)² – 4(1)(3)] / 2
    = [6 ± √(36 – 12)] / 2
    = [6 ± √24] / 2
    = [6 ± 2√6] / 2
    = 3 ± √6

Now, approximate √6:
  √6 ≈ 2.45

So the solutions become:
  x ≈ 3 + 2.45 = 5.45 and x ≈ 3 – 2.45 = 0.55

Rounded to two decimal places, the answers are:
  x = 5.45 or
  x = 0.55
$$ x = 5.45 $$ or $$ x = 0.55 $$

\[ -x^{2}+6 x-3=0 \] INSTRUCTION: Round your answers to two decimal places. Answer: \( x=\square \) or \( x=\square \)