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Solve by completing the square. -3w^(2)+42 w-33=0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. w=◻ or w=◻

Solve by completing the square.\newline−3w2+42w−33=0 -3 w^{2}+42 w-33=0 \newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinew=□ or w=□ w=\square \text { or } w= \square

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Q. Solve by completing the square.\newline−3w2+42w−33=0 -3 w^{2}+42 w-33=0 \newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinew=□ or w=□ w=\square \text { or } w= \square
  1. Write Equation Form: Write the equation in the form of aw2+bw=ca w^2 + b w = c. The given equation is −3w2+42w−33=0-3 w^2 + 42 w - 33 = 0.
  2. Divide and Simplify: Divide the entire equation by −3-3 to simplify the coefficients.\newline−3w2/−3+42w/−3−33/−3=0/−3-3w^2 / -3 + 42w / -3 - 33 / -3 = 0 / -3\newlinew2−14w+11=0w^2 - 14w + 11 = 0
  3. Move Constant Term: Move the constant term to the right side of the equation.\newlinew2−14w=−11w^2 - 14w = -11
  4. Complete the Square: Find the value to complete the square.\newlineTake half of the coefficient of ww, square it, and add it to both sides of the equation.\newline(−14/2)2=49(-14/2)^2 = 49\newlinew2−14w+49=−11+49w^2 - 14w + 49 = -11 + 49\newlinew2−14w+49=38w^2 - 14w + 49 = 38
  5. Factor and Simplify: Factor the left side of the equation and simplify the right side.\newline(w−7)2=38(w - 7)^2 = 38
  6. Take Square Root: Take the square root of both sides of the equation.\newline(w−7)2=±38\sqrt{(w - 7)^2} = \pm\sqrt{38}\newlinew−7=±38w - 7 = \pm\sqrt{38}
  7. Isolate Variable: Solve for ww by isolating the variable.w=7±38w = 7 \pm \sqrt{38}
  8. Calculate Approximate Values: Calculate the approximate decimal values of ww, rounded to the nearest hundredth.w≈7±6.16w \approx 7 \pm 6.16w≈7+6.16w \approx 7 + 6.16 or w≈7−6.16w \approx 7 - 6.16w≈13.16w \approx 13.16 or w≈0.84w \approx 0.84

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