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Solve by completing the square.\newliner2+16r=43r^2 + 16r = 43\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+16r=43r^2 + 16r = 43\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. Rewrite equation: Rewrite the equation in the form of r2+br=cr^2 + br = c. The given equation is already in this form: r2+16r=43r^2 + 16r = 43.
  2. Complete the square: Add the square of half the coefficient of rr to both sides to complete the square.\newlineThe coefficient of rr is 1616, so half of it is 88, and the square of 88 is 6464.\newlineAdd 6464 to both sides of the equation:\newliner2+16r+64=43+64r^2 + 16r + 64 = 43 + 64\newliner2+16r+64=107r^2 + 16r + 64 = 107
  3. Factor left side: Factor the left side of the equation.\newlineThe left side is a perfect square trinomial:\newline(r+8)2=107(r + 8)^2 = 107
  4. Take square root: Take the square root of both sides of the equation.\newline(r+8)2=±107\sqrt{(r + 8)^2} = \pm\sqrt{107}\newliner+8=±107r + 8 = \pm\sqrt{107}
  5. Isolate variable: Solve for rr by isolating the variable.\newlineSubtract 88 from both sides of the equation:\newliner=−8±107r = -8 \pm \sqrt{107}
  6. Simplify square root: Simplify the square root and round to the nearest hundredth if necessary.\newline107\sqrt{107} is an irrational number, so we will round it to the nearest hundredth:\newline107≈10.34\sqrt{107} \approx 10.34\newliner≈−8±10.34r \approx -8 \pm 10.34
  7. Find values of r: Find the two values of r.\newliner≈−8+10.34r \approx -8 + 10.34 implies r≈2.34r \approx 2.34\newliner≈−8−10.34r \approx -8 - 10.34 implies r≈−18.34r \approx -18.34\newlineValues of r: 2.342.34, −18.34-18.34

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