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Solve by completing the square.\newlines2+26s=−19s^2 + 26s = -19\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlines=s = _____ or s=s = _____

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Q. Solve by completing the square.\newlines2+26s=−19s^2 + 26s = -19\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlines=s = _____ or s=s = _____
  1. Write Equation Form: Write the equation in the form of s2+bs=cs^2 + bs = c. The given equation is already in this form: s2+26s=−19s^2 + 26s = -19.
  2. Move Constant Term: Move the constant term to the right side of the equation.\newlineAdd 1919 to both sides to isolate the s2s^2 and ss terms on the left.\newlines2+26s+19=0+19s^2 + 26s + 19 = 0 + 19\newlines2+26s=19s^2 + 26s = 19
  3. Complete the Square: Complete the square by adding the square of half the coefficient of ss to both sides.\newlineHalf of 2626 is 1313, and 13213^2 is 169169.\newlines2+26s+169=19+169s^2 + 26s + 169 = 19 + 169\newlines2+26s+169=188s^2 + 26s + 169 = 188
  4. Factor Perfect Square: Factor the left side of the equation as a perfect square.\newline(s+13)2=188(s + 13)^2 = 188
  5. Take Square Root: Take the square root of both sides of the equation.\newline(s+13)2=±188\sqrt{(s + 13)^2} = \pm\sqrt{188}\newlines+13=±188s + 13 = \pm\sqrt{188}
  6. Solve for ss: Solve for ss by subtracting 1313 from both sides.\newlines=−13±188s = -13 \pm \sqrt{188}\newlineTo find the decimal approximation, calculate 188≈13.71\sqrt{188} \approx 13.71.\newlines≈−13±13.71s \approx -13 \pm 13.71
  7. Find Values of \newliness: Find the two values of \newliness.\newline\newlines≈−13+13.71s \approx -13 + 13.71 implies \newlines≈0.71s \approx 0.71.\newline\newlines≈−13−13.71s \approx -13 - 13.71 implies \newlines≈−26.71s \approx -26.71.\newlineValues of \newliness: \newline0.71,−26.710.71, -26.71

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