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Solve by completing the square.\newlinew2+28w+37=0w^2 + 28w + 37 = 0\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+28w+37=0w^2 + 28w + 37 = 0\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. Set Up Equation: Write the equation in the form of w2+bw=cw^2 + bw = c.\newlineSubtract 3737 from both sides to set the equation up for completing the square.\newlinew2+28w+37−37=0−37w^2 + 28w + 37 - 37 = 0 - 37\newlinew2+28w=−37w^2 + 28w = -37
  2. Complete the Square: Find the number to add to both sides to complete the square.\newlineSince (282)2=196(\frac{28}{2})^2 = 196, add 196196 to both sides.\newlinew2+28w+196=−37+196w^2 + 28w + 196 = -37 + 196\newlinew2+28w+196=159w^2 + 28w + 196 = 159
  3. Factor Left Side: Factor the left side of the equation.\newline(w+14)2=159(w + 14)^2 = 159
  4. Take Square Root: Take the square root of both sides of the equation.\newline(w+14)2=±159\sqrt{(w + 14)^2} = \pm\sqrt{159}\newlinew+14=±159w + 14 = \pm\sqrt{159}
  5. Solve for ww: Solve for ww by subtracting 1414 from both sides.\newlinew=−14±159w = -14 \pm \sqrt{159}\newlineTo find the decimal approximation, calculate the square root of 159159 and round to the nearest hundredth.\newline159≈12.61\sqrt{159} \approx 12.61\newlinew≈−14±12.61w \approx -14 \pm 12.61
  6. Find Values of w: Find the two values of w.\newlinew≈−14+12.61w \approx -14 + 12.61 implies w≈−1.39w \approx -1.39.\newlinew≈−14−12.61w \approx -14 - 12.61 implies w≈−26.61w \approx -26.61.\newlineValues of w: −1.39-1.39, −26.61-26.61

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