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Solve by completing the square.\newliner2+26r=−29r^2 + 26r = -29\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+26r=−29r^2 + 26r = -29\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 Form: Write the equation in the form of r2+br=cr^2 + br = c. We have the equation r2+26r=−29r^2 + 26r = -29.
  2. Move Constant Term: Move the constant term to the right side of the equation.\newlineAdd 2929 to both sides to isolate the rr terms on the left.\newliner2+26r+29=0r^2 + 26r + 29 = 0
  3. Find Completing Number: Find the number to complete the square.\newlineTake half of the coefficient of rr, which is 2626, and square it. (26/2)2=132=169(26/2)^2 = 13^2 = 169.
  4. Add/Subtract Completing Number: Add and subtract the number found in Step 33 to the left side of the equation.\newliner2+26r+169−169=29r^2 + 26r + 169 - 169 = 29
  5. Factor Perfect Square Trinomial: Factor the perfect square trinomial on the left side of the equation. \newline(r+13)2−169=29(r + 13)^2 - 169 = 29
  6. Move Constant Term Right: Move the constant term to the right side to set up for taking the square root.\newline(r+13)2=29+169(r + 13)^2 = 29 + 169\newline(r+13)2=198(r + 13)^2 = 198
  7. Take Square Root: Take the square root of both sides of the equation.\newline(r+13)2=±198\sqrt{(r + 13)^2} = \pm\sqrt{198}\newliner+13=±198r + 13 = \pm\sqrt{198}
  8. Solve for r: Solve for r by subtracting 1313 from both sides.r=−13±198r = -13 \pm \sqrt{198}
  9. Simplify Square Root: Simplify the square root and round to the nearest hundredth if necessary.\newline198≈14.07\sqrt{198} \approx 14.07\newliner=−13±14.07r = -13 \pm 14.07
  10. Find Two Values: Find the two values of rr.r≈−13+14.07r \approx -13 + 14.07 implies r≈1.07r \approx 1.07.r≈−13−14.07r \approx -13 - 14.07 implies r≈−27.07r \approx -27.07.Values of rr: 1.071.07, −27.07-27.07

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