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Solve by completing the square.\newliner2−18r+49=0r^2 - 18r + 49 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliner=r = _____ or r=r = _____

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Q. Solve by completing the square.\newliner2−18r+49=0r^2 - 18r + 49 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliner=r = _____ or r=r = _____
  1. Write equation in standard form: Write the equation in the form of r2+br=cr^2 + br = c. The given equation is already in this form: r2−18r+49=0r^2 - 18r + 49 = 0.
  2. Move constant term: Move the constant term to the other side of the equation.\newlineSubtract 4949 from both sides to isolate the rr terms.\newliner2−18r=−49r^2 - 18r = -49
  3. Complete the square: Complete the square by adding the square of half the coefficient of rr to both sides.\newlineThe coefficient of rr is −18-18, so half of it is −9-9, and the square of −9-9 is 8181.\newlineAdd 8181 to both sides to complete the square.\newliner2−18r+81=−49+81r^2 − 18r + 81 = -49 + 81\newliner2−18r+81=32r^2 − 18r + 81 = 32
  4. Factor left side: Factor the left side of the equation.\newlineThe left side is a perfect square trinomial and can be factored into (r−9)2(r - 9)^2.\newline(r−9)2=32(r - 9)^2 = 32
  5. Take square root: Take the square root of both sides of the equation.\newline(r−9)2=±32\sqrt{(r - 9)^2} = \pm\sqrt{32}\newliner−9=±32r - 9 = \pm\sqrt{32}
  6. Solve for rr: Solve for rr by isolating the variable.\newlineAdd 99 to both sides of the equation to isolate rr.\newliner=9±32r = 9 \pm \sqrt{32}
  7. Simplify and finalize: Simplify the square root and write the final answers.\newline32\sqrt{32} can be simplified to 424\sqrt{2}, which is approximately 5.665.66 when rounded to the nearest hundredth.\newliner=9±42r = 9 \pm 4\sqrt{2}\newliner≈9+5.66r \approx 9 + 5.66 or r≈9−5.66r \approx 9 - 5.66\newliner≈14.66r \approx 14.66 or r≈3.34r \approx 3.34

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