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Solve by completing the square.\newlinew2+22w=31w^2 + 22w = 31\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinew=w = _____ or w=w = _____

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Q. Solve by completing the square.\newlinew2+22w=31w^2 + 22w = 31\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinew=w = _____ or w=w = _____
  1. Write Equation Form: Write the equation in the form of w2+bw=cw^2 + bw = c. The given equation is already in this form: w2+22w=31w^2 + 22w = 31.
  2. Move Constant Term: Move the constant term to the right side of the equation.\newlineSubtract 3131 from both sides to isolate the ww terms on the left side.\newlinew2+22w−31=0w^2 + 22w - 31 = 0\newlinew2+22w=31w^2 + 22w = 31
  3. Find Completing Square Number: Find the number to complete the square.\newlineTake half of the coefficient of ww, square it, and add it to both sides of the equation.\newline(222)2=112=121(\frac{22}{2})^2 = 11^2 = 121\newlinew2+22w+121=31+121w^2 + 22w + 121 = 31 + 121\newlinew2+22w+121=152w^2 + 22w + 121 = 152
  4. Factor Left Side: Factor the left side of the equation.\newlineThe left side is now a perfect square trinomial.\newline(w+11)2=152(w + 11)^2 = 152
  5. Take Square Root: Take the square root of both sides of the equation.\newline(w+11)2=±152\sqrt{(w + 11)^2} = \pm\sqrt{152}\newlinew+11=±152w + 11 = \pm\sqrt{152}
  6. Solve for ww: Solve for ww.\newlineSubtract 1111 from both sides to isolate ww.\newlinew=−11±152w = -11 \pm \sqrt{152}
  7. Simplify Square Root: Simplify the square root and round to the nearest hundredth if necessary.\newline152≈12.33\sqrt{152} \approx 12.33 (rounded to the nearest hundredth)\newlinew=−11±12.33w = -11 \pm 12.33
  8. Find Two Values: Find the two values of ww.w=−11+12.33≈1.33w = -11 + 12.33 \approx 1.33w=−11−12.33≈−23.33w = -11 - 12.33 \approx -23.33

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