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Solve by completing the square.\newlinet2−14t−43=0t^2 - 14t - 43 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinet=t = _____ or t=t = _____

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Q. Solve by completing the square.\newlinet2−14t−43=0t^2 - 14t - 43 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinet=t = _____ or t=t = _____
  1. Rewrite equation: Rewrite the equation in the form of t2+bt=ct^2 + bt = c.\newlineAdd 4343 to both sides to set the equation up for completing the square.\newlinet2−14t−43+43=0+43t^2 - 14t - 43 + 43 = 0 + 43\newlinet2−14t=43t^2 - 14t = 43
  2. Add 4343: Choose the number to add to both sides to complete the square.\newlineSince (−142)2=49(-\frac{14}{2})^2 = 49, add 4949 to both sides.\newlinet2−14t+49=43+49t^2 − 14t + 49 = 43 + 49\newlinet2−14t+49=92t^2 − 14t + 49 = 92
  3. Choose number to add: Factor the left side of the equation. \newline(t−7)2=92(t - 7)^2 = 92
  4. Factor left side: Take the square root of both sides of the equation.\newline(t−7)2=±92\sqrt{(t − 7)^2} = \pm\sqrt{92}\newlinet−7=±92t − 7 = \pm\sqrt{92}
  5. Take square root: Solve for tt.\newlineAdd 77 to both sides of the equation to isolate tt.\newlinet−7+7=±92+7t - 7 + 7 = \pm\sqrt{92} + 7\newlinet=7±92t = 7 \pm \sqrt{92}
  6. Solve for t: Calculate the approximate decimal values of tt, rounded to the nearest hundredth.92\sqrt{92} is approximately 9.599.59.t≈7±9.59t \approx 7 \pm 9.59t≈7+9.59t \approx 7 + 9.59 or t≈7−9.59t \approx 7 - 9.59t≈16.59t \approx 16.59 or t≈−2.59t \approx -2.59

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