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Solve by completing the square.\newlines2+18s=−29s^2 + 18s = -29\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+18s=−29s^2 + 18s = -29\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+18s=−29s^2 + 18s = -29.
  2. Move Constant Term: Move the constant term to the other side of the equation.\newlineAdd 2929 to both sides to isolate the s2s^2 and ss terms.\newlines2+18s+29=0+29s^2 + 18s + 29 = 0 + 29\newlines2+18s=29s^2 + 18s = 29
  3. Find Completing Square Number: Find the number to complete the square.\newlineTake half of the coefficient of ss, square it, and add it to both sides of the equation.\newline(18/2)2=92=81(18/2)^2 = 9^2 = 81\newlines2+18s+81=29+81s^2 + 18s + 81 = 29 + 81\newlines2+18s+81=110s^2 + 18s + 81 = 110
  4. Factor Left Side: Factor the left side of the equation.\newlineThe left side is now a perfect square trinomial.\newline(s+9)2=110(s + 9)^2 = 110
  5. Take Square Root: Take the square root of both sides of the equation.\newline(s+9)2=±110\sqrt{(s + 9)^2} = \pm\sqrt{110}\newlines+9=±110s + 9 = \pm\sqrt{110}
  6. Solve for ss: Solve for ss.\newlineSubtract 99 from both sides to isolate ss.\newlines=−9±110s = -9 \pm \sqrt{110}
  7. Simplify Square Root: Simplify the square root if necessary and round to the nearest hundredth.\newline110≈10.49\sqrt{110} \approx 10.49\newlines=−9±10.49s = -9 \pm 10.49\newlines≈−9+10.49s \approx -9 + 10.49 or s≈−9−10.49s \approx -9 - 10.49\newlines≈1.49s \approx 1.49 or s≈−19.49s \approx -19.49

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